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<li id="toc-Sirens" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Sirens"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1</span> <span>Sirens</span> </div> </a> <ul id="toc-Sirens-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Astronomy" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Astronomy"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2</span> <span>Astronomy</span> </div> </a> <ul id="toc-Astronomy-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Radar" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Radar"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.3</span> <span>Radar</span> </div> </a> <ul id="toc-Radar-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Medical" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Medical"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.4</span> <span>Medical</span> </div> </a> <ul id="toc-Medical-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Flow_measurement" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Flow_measurement"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.5</span> <span>Flow measurement</span> </div> </a> <ul id="toc-Flow_measurement-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Velocity_profile_measurement" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Velocity_profile_measurement"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.6</span> <span>Velocity profile measurement</span> </div> </a> <ul id="toc-Velocity_profile_measurement-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Satellites" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Satellites"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.7</span> <span>Satellites</span> </div> </a> <ul id="toc-Satellites-sublist" class="vector-toc-list"> <li id="toc-Satellite_navigation" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Satellite_navigation"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.7.1</span> <span>Satellite navigation</span> </div> </a> <ul id="toc-Satellite_navigation-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Satellite_communication" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Satellite_communication"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.7.2</span> <span>Satellite communication</span> </div> </a> <ul id="toc-Satellite_communication-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Audio" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Audio"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.8</span> <span>Audio</span> </div> </a> <ul id="toc-Audio-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Vibration_measurement" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Vibration_measurement"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.9</span> <span>Vibration measurement</span> </div> </a> <ul id="toc-Vibration_measurement-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Robotics" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Robotics"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.10</span> <span>Robotics</span> </div> </a> <ul id="toc-Robotics-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Inverse_Doppler_effect" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Inverse_Doppler_effect"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Inverse Doppler effect</span> </div> </a> <ul id="toc-Inverse_Doppler_effect-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Primary_sources" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Primary_sources"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Primary sources</span> </div> </a> <ul id="toc-Primary_sources-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Further_reading" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Further_reading"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>Further reading</span> </div> </a> <ul id="toc-Further_reading-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">10</span> <span>External links</span> </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Toggle the table of contents</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Doppler effect</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. Available in 85 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-85" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">85 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Doppler-effek" title="Doppler-effek – Afrikaans" lang="af" hreflang="af" data-title="Doppler-effek" data-language-autonym="Afrikaans" data-language-local-name="Afrikaans" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-als mw-list-item"><a href="https://als.wikipedia.org/wiki/Doppler-Effekt" title="Doppler-Effekt – Alemannic" lang="gsw" hreflang="gsw" data-title="Doppler-Effekt" data-language-autonym="Alemannisch" data-language-local-name="Alemannic" class="interlanguage-link-target"><span>Alemannisch</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%AA%D8%A3%D8%AB%D9%8A%D8%B1_%D8%AF%D9%88%D8%A8%D9%84%D8%B1" title="تأثير دوبلر – Arabic" lang="ar" hreflang="ar" data-title="تأثير دوبلر" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-as mw-list-item"><a href="https://as.wikipedia.org/wiki/%E0%A6%A1%27%E0%A6%AA%E0%A6%B2%E0%A6%BE%E0%A7%B0_%E0%A6%AA%E0%A7%8D%E0%A7%B0%E0%A6%AD%E0%A6%BE%E0%A7%B1" title="ড'পলাৰ প্ৰভাৱ – Assamese" lang="as" hreflang="as" data-title="ড'পলাৰ প্ৰভাৱ" data-language-autonym="অসমীয়া" data-language-local-name="Assamese" class="interlanguage-link-target"><span>অসমীয়া</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Efeutu_Doppler" title="Efeutu Doppler – Asturian" lang="ast" hreflang="ast" data-title="Efeutu Doppler" data-language-autonym="Asturianu" data-language-local-name="Asturian" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Dopler_effekti" title="Dopler effekti – Azerbaijani" lang="az" hreflang="az" data-title="Dopler effekti" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbaijani" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%A1%E0%A6%AA%E0%A6%B2%E0%A6%BE%E0%A6%B0_%E0%A6%95%E0%A7%8D%E0%A6%B0%E0%A6%BF%E0%A6%AF%E0%A6%BC%E0%A6%BE" title="ডপলার ক্রিয়া – Bangla" lang="bn" hreflang="bn" data-title="ডপলার ক্রিয়া" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%AD%D1%84%D0%B5%D0%BA%D1%82_%D0%94%D0%BE%D0%BF%D0%BB%D0%B5%D1%80%D0%B0" title="Эфект Доплера – Belarusian" lang="be" hreflang="be" data-title="Эфект Доплера" data-language-autonym="Беларуская" data-language-local-name="Belarusian" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%94%D0%BE%D0%BF%D0%BB%D0%B5%D1%80%D0%BE%D0%B2_%D0%B5%D1%84%D0%B5%D0%BA%D1%82" title="Доплеров ефект – Bulgarian" lang="bg" hreflang="bg" data-title="Доплеров ефект" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Dopplerov_efekt" title="Dopplerov efekt – Bosnian" lang="bs" hreflang="bs" data-title="Dopplerov efekt" data-language-autonym="Bosanski" data-language-local-name="Bosnian" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-br mw-list-item"><a href="https://br.wikipedia.org/wiki/Efed_Doppler" title="Efed Doppler – Breton" lang="br" hreflang="br" data-title="Efed Doppler" data-language-autonym="Brezhoneg" data-language-local-name="Breton" class="interlanguage-link-target"><span>Brezhoneg</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Efecte_Doppler" title="Efecte Doppler – Catalan" lang="ca" hreflang="ca" data-title="Efecte Doppler" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%94%D0%BE%D0%BF%D0%BB%D0%B5%D1%80_%D1%8D%D1%84%D1%84%D0%B5%D0%BA%D1%87%C4%95" title="Доплер эффекчĕ – Chuvash" lang="cv" hreflang="cv" data-title="Доплер эффекчĕ" data-language-autonym="Чӑвашла" data-language-local-name="Chuvash" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Doppler%C5%AFv_jev" title="Dopplerův jev – Czech" lang="cs" hreflang="cs" data-title="Dopplerův jev" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Effaith_Doppler" title="Effaith Doppler – Welsh" lang="cy" hreflang="cy" data-title="Effaith Doppler" data-language-autonym="Cymraeg" data-language-local-name="Welsh" class="interlanguage-link-target"><span>Cymraeg</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Dopplereffekt" title="Dopplereffekt – Danish" lang="da" hreflang="da" data-title="Dopplereffekt" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Doppler-Effekt" title="Doppler-Effekt – German" lang="de" hreflang="de" data-title="Doppler-Effekt" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Doppleri_efekt" title="Doppleri efekt – Estonian" lang="et" hreflang="et" data-title="Doppleri efekt" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%A6%CE%B1%CE%B9%CE%BD%CF%8C%CE%BC%CE%B5%CE%BD%CE%BF_%CE%9D%CF%84%CF%8C%CF%80%CE%BB%CE%B5%CF%81" title="Φαινόμενο Ντόπλερ – Greek" lang="el" hreflang="el" data-title="Φαινόμενο Ντόπλερ" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Efecto_Doppler" title="Efecto Doppler – Spanish" lang="es" hreflang="es" data-title="Efecto Doppler" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Efiko_de_Doppler" title="Efiko de Doppler – Esperanto" lang="eo" hreflang="eo" data-title="Efiko de Doppler" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Doppler_efektua" title="Doppler efektua – Basque" lang="eu" hreflang="eu" data-title="Doppler efektua" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%A7%D8%AB%D8%B1_%D8%AF%D9%88%D9%BE%D9%84%D8%B1" title="اثر دوپلر – Persian" lang="fa" hreflang="fa" data-title="اثر دوپلر" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Effet_Doppler" title="Effet Doppler – French" lang="fr" hreflang="fr" data-title="Effet Doppler" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Iarmhairt_Doppler" title="Iarmhairt Doppler – Irish" lang="ga" hreflang="ga" data-title="Iarmhairt Doppler" data-language-autonym="Gaeilge" data-language-local-name="Irish" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Efecto_Doppler" title="Efecto Doppler – Galician" lang="gl" hreflang="gl" data-title="Efecto Doppler" data-language-autonym="Galego" data-language-local-name="Galician" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EB%8F%84%ED%94%8C%EB%9F%AC_%ED%9A%A8%EA%B3%BC" title="도플러 효과 – Korean" lang="ko" hreflang="ko" data-title="도플러 효과" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D4%B4%D5%B8%D5%BA%D5%AC%D5%A5%D6%80%D5%AB_%D5%A7%D6%86%D5%A5%D5%AF%D5%BF" title="Դոպլերի էֆեկտ – Armenian" lang="hy" hreflang="hy" data-title="Դոպլերի էֆեկտ" data-language-autonym="Հայերեն" data-language-local-name="Armenian" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%A1%E0%A5%89%E0%A4%AA%E0%A5%8D%E0%A4%B2%E0%A4%B0_%E0%A4%AA%E0%A5%8D%E0%A4%B0%E0%A4%AD%E0%A4%BE%E0%A4%B5" title="डॉप्लर प्रभाव – Hindi" lang="hi" hreflang="hi" data-title="डॉप्लर प्रभाव" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Dopplerov_efekt" title="Dopplerov efekt – Croatian" lang="hr" hreflang="hr" data-title="Dopplerov efekt" data-language-autonym="Hrvatski" data-language-local-name="Croatian" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Efek_Doppler" title="Efek Doppler – Indonesian" lang="id" hreflang="id" data-title="Efek Doppler" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Dopplerhrif" title="Dopplerhrif – Icelandic" lang="is" hreflang="is" data-title="Dopplerhrif" data-language-autonym="Íslenska" data-language-local-name="Icelandic" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Effetto_Doppler" title="Effetto Doppler – Italian" lang="it" hreflang="it" data-title="Effetto Doppler" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%90%D7%A4%D7%A7%D7%98_%D7%93%D7%95%D7%A4%D7%9C%D7%A8" title="אפקט דופלר – Hebrew" lang="he" hreflang="he" data-title="אפקט דופלר" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-kn mw-list-item"><a href="https://kn.wikipedia.org/wiki/%E0%B2%A1%E0%B2%BE%E0%B2%AA%E0%B3%8D%E0%B2%B2%E0%B2%B0%E0%B3%8D_%E0%B2%AA%E0%B2%B0%E0%B2%BF%E0%B2%A3%E0%B2%BE%E0%B2%AE" title="ಡಾಪ್ಲರ್ ಪರಿಣಾಮ – Kannada" lang="kn" hreflang="kn" data-title="ಡಾಪ್ಲರ್ ಪರಿಣಾಮ" data-language-autonym="ಕನ್ನಡ" data-language-local-name="Kannada" class="interlanguage-link-target"><span>ಕನ್ನಡ</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%93%E1%83%9D%E1%83%9E%E1%83%9A%E1%83%94%E1%83%A0%E1%83%98%E1%83%A1_%E1%83%94%E1%83%A4%E1%83%94%E1%83%A5%E1%83%A2%E1%83%98" title="დოპლერის ეფექტი – Georgian" lang="ka" hreflang="ka" data-title="დოპლერის ეფექტი" data-language-autonym="ქართული" data-language-local-name="Georgian" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%94%D0%BE%D0%BF%D0%BB%D0%B5%D1%80_%D1%8D%D1%84%D1%84%D0%B5%D0%BA%D1%82%D1%96" title="Доплер эффекті – Kazakh" lang="kk" hreflang="kk" data-title="Доплер эффекті" data-language-autonym="Қазақша" data-language-local-name="Kazakh" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-sw mw-list-item"><a href="https://sw.wikipedia.org/wiki/Athari_ya_Doppler" title="Athari ya Doppler – Swahili" lang="sw" hreflang="sw" data-title="Athari ya Doppler" data-language-autonym="Kiswahili" data-language-local-name="Swahili" class="interlanguage-link-target"><span>Kiswahili</span></a></li><li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/Ef%C3%A8_Doppler" title="Efè Doppler – Haitian Creole" lang="ht" hreflang="ht" data-title="Efè Doppler" data-language-autonym="Kreyòl ayisyen" data-language-local-name="Haitian Creole" class="interlanguage-link-target"><span>Kreyòl ayisyen</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Effectus_Doppler" title="Effectus Doppler – Latin" lang="la" hreflang="la" data-title="Effectus Doppler" data-language-autonym="Latina" data-language-local-name="Latin" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Doplera_efekts" title="Doplera efekts – Latvian" lang="lv" hreflang="lv" data-title="Doplera efekts" data-language-autonym="Latviešu" data-language-local-name="Latvian" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Doplerio_efektas" title="Doplerio efektas – Lithuanian" lang="lt" hreflang="lt" data-title="Doplerio efektas" data-language-autonym="Lietuvių" data-language-local-name="Lithuanian" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Doppler-effektus" title="Doppler-effektus – Hungarian" lang="hu" hreflang="hu" data-title="Doppler-effektus" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%94%D0%BE%D0%BF%D0%BB%D0%B5%D1%80%D0%BE%D0%B2_%D0%B5%D1%84%D0%B5%D0%BA%D1%82" title="Доплеров ефект – Macedonian" lang="mk" hreflang="mk" data-title="Доплеров ефект" data-language-autonym="Македонски" data-language-local-name="Macedonian" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%A1%E0%B5%8B%E0%B4%AA%E0%B5%8D%E0%B4%B2%E0%B5%BC_%E0%B4%AA%E0%B5%8D%E0%B4%B0%E0%B4%AD%E0%B4%BE%E0%B4%B5%E0%B4%82" title="ഡോപ്ലർ പ്രഭാവം – Malayalam" lang="ml" hreflang="ml" data-title="ഡോപ്ലർ പ്രഭാവം" data-language-autonym="മലയാളം" data-language-local-name="Malayalam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Kesan_Doppler" title="Kesan Doppler – Malay" lang="ms" hreflang="ms" data-title="Kesan Doppler" data-language-autonym="Bahasa Melayu" data-language-local-name="Malay" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-my mw-list-item"><a href="https://my.wikipedia.org/wiki/%E1%80%92%E1%80%B1%E1%80%AB%E1%80%B7%E1%80%95%E1%80%9C%E1%80%AC_%E1%80%A1%E1%80%80%E1%80%BB%E1%80%AD%E1%80%AF%E1%80%B8%E1%80%9E%E1%80%80%E1%80%BA%E1%80%9B%E1%80%B1%E1%80%AC%E1%80%80%E1%80%BA%E1%80%99%E1%80%BE%E1%80%AF" title="ဒေါ့ပလာ အကျိုးသက်ရောက်မှု – Burmese" lang="my" hreflang="my" data-title="ဒေါ့ပလာ အကျိုးသက်ရောက်မှု" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="Burmese" class="interlanguage-link-target"><span>မြန်မာဘာသာ</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Dopplereffect" title="Dopplereffect – Dutch" lang="nl" hreflang="nl" data-title="Dopplereffect" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E3%83%89%E3%83%83%E3%83%97%E3%83%A9%E3%83%BC%E5%8A%B9%E6%9E%9C" title="ドップラー効果 – Japanese" lang="ja" hreflang="ja" data-title="ドップラー効果" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Dopplereffekt" title="Dopplereffekt – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Dopplereffekt" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Dopplereffekten" title="Dopplereffekten – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Dopplereffekten" data-language-autonym="Norsk nynorsk" data-language-local-name="Norwegian Nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-nov mw-list-item"><a href="https://nov.wikipedia.org/wiki/Doppler-efekte" title="Doppler-efekte – Novial" lang="nov" hreflang="nov" data-title="Doppler-efekte" data-language-autonym="Novial" data-language-local-name="Novial" class="interlanguage-link-target"><span>Novial</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Ef%C3%A8cte_Doppler" title="Efècte Doppler – Occitan" lang="oc" hreflang="oc" data-title="Efècte Doppler" data-language-autonym="Occitan" data-language-local-name="Occitan" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-or mw-list-item"><a href="https://or.wikipedia.org/wiki/%E0%AC%A1%E0%AD%8B%E0%AC%AA%E0%AD%8D%E0%AC%B2%E0%AC%B0%E0%AD%8D_%E0%AC%AA%E0%AD%8D%E0%AC%B0%E0%AC%AD%E0%AC%BE%E0%AC%AC" title="ଡୋପ୍ଲର୍ ପ୍ରଭାବ – Odia" lang="or" hreflang="or" data-title="ଡୋପ୍ଲର୍ ପ୍ରଭାବ" data-language-autonym="ଓଡ଼ିଆ" data-language-local-name="Odia" class="interlanguage-link-target"><span>ଓଡ଼ିଆ</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Doppler_effekti" title="Doppler effekti – Uzbek" lang="uz" hreflang="uz" data-title="Doppler effekti" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Uzbek" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%A1%E0%A8%BE%E0%A8%AA%E0%A8%B2%E0%A8%B0_%E0%A8%AA%E0%A9%8D%E0%A8%B0%E0%A8%AD%E0%A8%BE%E0%A8%B5" title="ਡਾਪਲਰ ਪ੍ਰਭਾਵ – Punjabi" lang="pa" hreflang="pa" data-title="ਡਾਪਲਰ ਪ੍ਰਭਾਵ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="Punjabi" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pnb mw-list-item"><a href="https://pnb.wikipedia.org/wiki/%DA%88%D9%88%D9%BE%D9%84%D8%B1_%D8%A7%DB%8C%D9%81%DA%A9%D9%B9" title="ڈوپلر ایفکٹ – Western Punjabi" lang="pnb" hreflang="pnb" data-title="ڈوپلر ایفکٹ" data-language-autonym="پنجابی" data-language-local-name="Western Punjabi" class="interlanguage-link-target"><span>پنجابی</span></a></li><li class="interlanguage-link interwiki-pms mw-list-item"><a href="https://pms.wikipedia.org/wiki/Efet_Doppler" title="Efet Doppler – Piedmontese" lang="pms" hreflang="pms" data-title="Efet Doppler" data-language-autonym="Piemontèis" data-language-local-name="Piedmontese" class="interlanguage-link-target"><span>Piemontèis</span></a></li><li class="interlanguage-link interwiki-pl badge-Q17437796 badge-featuredarticle mw-list-item" title="featured article badge"><a href="https://pl.wikipedia.org/wiki/Efekt_Dopplera" title="Efekt Dopplera – Polish" lang="pl" hreflang="pl" data-title="Efekt Dopplera" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Efeito_Doppler" title="Efeito Doppler – Portuguese" lang="pt" hreflang="pt" data-title="Efeito Doppler" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Efectul_Doppler" title="Efectul Doppler – Romanian" lang="ro" hreflang="ro" data-title="Efectul Doppler" data-language-autonym="Română" data-language-local-name="Romanian" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%AD%D1%84%D1%84%D0%B5%D0%BA%D1%82_%D0%94%D0%BE%D0%BF%D0%BB%D0%B5%D1%80%D0%B0" title="Эффект Доплера – Russian" lang="ru" hreflang="ru" data-title="Эффект Доплера" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Efekti_i_Dopplerit" title="Efekti i Dopplerit – Albanian" lang="sq" hreflang="sq" data-title="Efekti i Dopplerit" data-language-autonym="Shqip" data-language-local-name="Albanian" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-si mw-list-item"><a href="https://si.wikipedia.org/wiki/%E0%B6%A9%E0%B7%9C%E0%B6%B4%E0%B7%8A%E0%B6%BD%E0%B6%BB%E0%B7%8A_%E0%B6%86%E0%B6%A0%E0%B6%BB%E0%B6%AB%E0%B6%BA" title="ඩොප්ලර් ආචරණය – Sinhala" lang="si" hreflang="si" data-title="ඩොප්ලර් ආචරණය" data-language-autonym="සිංහල" data-language-local-name="Sinhala" class="interlanguage-link-target"><span>සිංහල</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Doppler_effect" title="Doppler effect – Simple English" lang="en-simple" hreflang="en-simple" data-title="Doppler effect" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Dopplerov_jav" title="Dopplerov jav – Slovak" lang="sk" hreflang="sk" data-title="Dopplerov jav" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Dopplerjev_pojav" title="Dopplerjev pojav – Slovenian" lang="sl" hreflang="sl" data-title="Dopplerjev pojav" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%DA%A9%D8%A7%D8%B1%DB%8C%DA%AF%DB%95%D8%B1%DB%8C%DB%8C_%D8%AF%DB%86%D9%BE%D9%84%DB%95%D8%B1" title="کاریگەریی دۆپلەر – Central Kurdish" lang="ckb" hreflang="ckb" data-title="کاریگەریی دۆپلەر" data-language-autonym="کوردی" data-language-local-name="Central Kurdish" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%94%D0%BE%D0%BF%D0%BB%D0%B5%D1%80%D0%BE%D0%B2_%D0%B5%D1%84%D0%B5%D0%BA%D0%B0%D1%82" title="Доплеров ефекат – Serbian" lang="sr" hreflang="sr" data-title="Доплеров ефекат" data-language-autonym="Српски / srpski" data-language-local-name="Serbian" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Dopplerov_efekat" title="Dopplerov efekat – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Dopplerov efekat" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Serbo-Croatian" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Doppler-ilmi%C3%B6" title="Doppler-ilmiö – Finnish" lang="fi" hreflang="fi" data-title="Doppler-ilmiö" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Dopplereffekt" title="Dopplereffekt – Swedish" lang="sv" hreflang="sv" data-title="Dopplereffekt" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Epektong_Doppler" title="Epektong Doppler – Tagalog" lang="tl" hreflang="tl" data-title="Epektong Doppler" data-language-autonym="Tagalog" data-language-local-name="Tagalog" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%9F%E0%AE%BE%E0%AE%AA%E0%AF%8D%E0%AE%B3%E0%AE%B0%E0%AF%8D_%E0%AE%B5%E0%AE%BF%E0%AE%B3%E0%AF%88%E0%AE%B5%E0%AF%81" title="டாப்ளர் விளைவு – Tamil" lang="ta" hreflang="ta" data-title="டாப்ளர் விளைவு" data-language-autonym="தமிழ்" data-language-local-name="Tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-tt mw-list-item"><a href="https://tt.wikipedia.org/wiki/%D0%94%D0%BE%D0%BF%D0%BF%D0%BB%D0%B5%D1%80_%D1%8D%D1%84%D1%84%D0%B5%D0%BA%D1%82%D1%8B" title="Допплер эффекты – Tatar" lang="tt" hreflang="tt" data-title="Допплер эффекты" data-language-autonym="Татарча / tatarça" data-language-local-name="Tatar" class="interlanguage-link-target"><span>Татарча / tatarça</span></a></li><li class="interlanguage-link interwiki-te mw-list-item"><a href="https://te.wikipedia.org/wiki/%E0%B0%A1%E0%B0%BE%E0%B0%AA%E0%B1%8D%E0%B0%B2%E0%B0%B0%E0%B1%8D_%E0%B0%AA%E0%B1%8D%E0%B0%B0%E0%B0%AD%E0%B0%BE%E0%B0%B5%E0%B0%82" title="డాప్లర్ ప్రభావం – Telugu" lang="te" hreflang="te" data-title="డాప్లర్ ప్రభావం" data-language-autonym="తెలుగు" data-language-local-name="Telugu" class="interlanguage-link-target"><span>తెలుగు</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%9B%E0%B8%A3%E0%B8%B2%E0%B8%81%E0%B8%8F%E0%B8%81%E0%B8%B2%E0%B8%A3%E0%B8%93%E0%B9%8C%E0%B8%94%E0%B9%87%E0%B8%AD%E0%B8%9E%E0%B9%80%E0%B8%9E%E0%B8%A5%E0%B8%AD%E0%B8%A3%E0%B9%8C" title="ปรากฏการณ์ด็อพเพลอร์ – Thai" lang="th" hreflang="th" data-title="ปรากฏการณ์ด็อพเพลอร์" data-language-autonym="ไทย" data-language-local-name="Thai" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Doppler_etkisi" title="Doppler etkisi – Turkish" lang="tr" hreflang="tr" data-title="Doppler etkisi" data-language-autonym="Türkçe" data-language-local-name="Turkish" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%95%D1%84%D0%B5%D0%BA%D1%82_%D0%94%D0%BE%D0%BF%D0%BB%D0%B5%D1%80%D0%B0" title="Ефект Доплера – Ukrainian" lang="uk" hreflang="uk" 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</div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">From Wikipedia, the free encyclopedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Frequency change of a wave for observer relative to its source</div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">For the music project, see <a href="/wiki/Dopplereffekt" title="Dopplereffekt">Dopplereffekt</a>.</div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">"Doppler" redirects here. For other uses, see <a href="/wiki/Doppler_(disambiguation)" class="mw-disambig" title="Doppler (disambiguation)">Doppler (disambiguation)</a>.</div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Doppler_effect_diagrammatic.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/7f/Doppler_effect_diagrammatic.svg/260px-Doppler_effect_diagrammatic.svg.png" decoding="async" width="260" height="83" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/7f/Doppler_effect_diagrammatic.svg/390px-Doppler_effect_diagrammatic.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/7f/Doppler_effect_diagrammatic.svg/520px-Doppler_effect_diagrammatic.svg.png 2x" data-file-width="744" data-file-height="238" /></a><figcaption>Change of <a href="/wiki/Wavelength" title="Wavelength">wavelength</a> caused by motion of the source.</figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Dopplerfrequenz.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/90/Dopplerfrequenz.gif/260px-Dopplerfrequenz.gif" decoding="async" width="260" height="52" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/90/Dopplerfrequenz.gif/390px-Dopplerfrequenz.gif 1.5x, //upload.wikimedia.org/wikipedia/commons/9/90/Dopplerfrequenz.gif 2x" data-file-width="500" data-file-height="100" /></a><figcaption>An animation illustrating how the Doppler effect causes a car engine or siren to sound higher in pitch when it is approaching than when it is receding. The red circles represent sound waves.<style data-mw-deduplicate="TemplateStyles:r1235681985">.mw-parser-output .side-box{margin:4px 0;box-sizing:border-box;border:1px solid #aaa;font-size:88%;line-height:1.25em;background-color:var(--background-color-interactive-subtle,#f8f9fa);display:flow-root}.mw-parser-output .side-box-abovebelow,.mw-parser-output .side-box-text{padding:0.25em 0.9em}.mw-parser-output .side-box-image{padding:2px 0 2px 0.9em;text-align:center}.mw-parser-output .side-box-imageright{padding:2px 0.9em 2px 0;text-align:center}@media(min-width:500px){.mw-parser-output .side-box-flex{display:flex;align-items:center}.mw-parser-output .side-box-text{flex:1;min-width:0}}@media(min-width:720px){.mw-parser-output .side-box{width:238px}.mw-parser-output .side-box-right{clear:right;float:right;margin-left:1em}.mw-parser-output .side-box-left{margin-right:1em}}</style><style data-mw-deduplicate="TemplateStyles:r1096940132">.mw-parser-output .listen .side-box-text{line-height:1.1em}.mw-parser-output .listen-plain{border:none;background:transparent}.mw-parser-output .listen-embedded{width:100%;margin:0;border-width:1px 0 0 0;background:transparent}.mw-parser-output .listen-header{padding:2px}.mw-parser-output .listen-embedded .listen-header{padding:2px 0}.mw-parser-output .listen-file-header{padding:4px 0}.mw-parser-output .listen .description{padding-top:2px}.mw-parser-output .listen .mw-tmh-player{max-width:100%}@media(max-width:719px){.mw-parser-output .listen{clear:both}}@media(min-width:720px){.mw-parser-output .listen:not(.listen-noimage){width:320px}.mw-parser-output .listen-left{overflow:visible;float:left}.mw-parser-output .listen-center{float:none;margin-left:auto;margin-right:auto}}</style><div class="side-box side-box-right listen noprint listen-center"><style data-mw-deduplicate="TemplateStyles:r1126788409">.mw-parser-output .plainlist ol,.mw-parser-output .plainlist ul{line-height:inherit;list-style:none;margin:0;padding:0}.mw-parser-output .plainlist ol li,.mw-parser-output .plainlist ul li{margin-bottom:0}</style> <div class="side-box-flex"> <div class="side-box-image"><figure class="mw-halign-center" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/8/87/Gnome-mime-sound-openclipart.svg/50px-Gnome-mime-sound-openclipart.svg.png" decoding="async" width="50" height="50" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/87/Gnome-mime-sound-openclipart.svg/75px-Gnome-mime-sound-openclipart.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/87/Gnome-mime-sound-openclipart.svg/100px-Gnome-mime-sound-openclipart.svg.png 2x" data-file-width="160" data-file-height="160" /></span><figcaption></figcaption></figure></div> <div class="side-box-text plainlist"><div class="haudio"> <div class="listen-file-header"><a href="/wiki/File:Speeding-car-horn_doppler_effect_sample.ogg" title="File:Speeding-car-horn doppler effect sample.ogg">Passing car horn</a></div> <div><span typeof="mw:File"><span><audio id="mwe_player_0" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="232" style="width:232px;" data-durationhint="3" data-mwtitle="Speeding-car-horn_doppler_effect_sample.ogg" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/9/90/Speeding-car-horn_doppler_effect_sample.ogg" type="audio/ogg; codecs="vorbis"" data-width="0" data-height="0" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/9/90/Speeding-car-horn_doppler_effect_sample.ogg/Speeding-car-horn_doppler_effect_sample.ogg.mp3" type="audio/mpeg" data-transcodekey="mp3" data-width="0" data-height="0" /><track src="https://commons.wikimedia.org/w/api.php?action=timedtext&title=File%3ASpeeding-car-horn_doppler_effect_sample.ogg&lang=en&trackformat=vtt&origin=%2A" kind="subtitles" type="text/vtt" srclang="en" label="English ‪(en)‬" data-dir="ltr" /></audio></span></span></div> <div class="description"></div></div></div></div> </div> </figcaption></figure><p>The <b>Doppler effect</b> (also <b>Doppler shift</b>) is the change in the <a href="/wiki/Frequency" title="Frequency">frequency</a> of a <a href="/wiki/Wave" title="Wave">wave</a> in relation to an observer who is moving relative to the source of the wave.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Giordano_3-0" class="reference"><a href="#cite_note-Giordano-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> The <i>Doppler effect</i> is named after the physicist <a href="/wiki/Christian_Doppler" title="Christian Doppler">Christian Doppler</a>, who described the phenomenon in 1842. A common example of Doppler shift is the change of <a href="/wiki/Pitch_(music)" title="Pitch (music)">pitch</a> heard when a <a href="/wiki/Vehicle" title="Vehicle">vehicle</a> sounding a horn approaches and recedes from an observer. Compared to the emitted frequency, the received frequency is higher during the approach, identical at the instant of passing by, and lower during the recession.<sup id="cite_ref-Possel_4-0" class="reference"><a href="#cite_note-Possel-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p><p>When the source of the sound wave is moving towards the observer, each successive cycle of the wave is emitted from a position closer to the observer than the previous cycle.<sup id="cite_ref-Possel_4-1" class="reference"><a href="#cite_note-Possel-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Henderson_5-0" class="reference"><a href="#cite_note-Henderson-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> Hence, from the observer's perspective, the time between cycles is reduced, meaning the frequency is increased. Conversely, if the source of the sound wave is moving away from the observer, each cycle of the wave is emitted from a position farther from the observer than the previous cycle, so the arrival time between successive cycles is increased, thus reducing the frequency. </p><p>For waves that propagate in a medium, such as <a href="/wiki/Sound" title="Sound">sound</a> waves, the <a href="/wiki/Velocity" title="Velocity">velocity</a> of the observer and of the source are relative to the medium in which the waves are transmitted.<sup id="cite_ref-Giordano_3-1" class="reference"><a href="#cite_note-Giordano-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> The total Doppler effect in such cases may therefore result from motion of the source, motion of the observer, motion of the medium, or any combination thereof. For waves propagating in <a href="/wiki/Vacuum" title="Vacuum">vacuum</a>, as is possible for <a href="/wiki/Electromagnetic_waves" class="mw-redirect" title="Electromagnetic waves">electromagnetic waves</a> or <a href="/wiki/Gravitational_wave" title="Gravitational wave">gravitational waves</a>, only the difference in velocity between the observer and the source needs to be considered. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="History">History</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Doppler_effect&action=edit&section=1" title="Edit section: History"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Picture_of_the_first_%27wall_formula%27_in_the_city_of_Utrecht_01.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/43/Picture_of_the_first_%27wall_formula%27_in_the_city_of_Utrecht_01.jpg/220px-Picture_of_the_first_%27wall_formula%27_in_the_city_of_Utrecht_01.jpg" decoding="async" width="220" height="165" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/43/Picture_of_the_first_%27wall_formula%27_in_the_city_of_Utrecht_01.jpg/330px-Picture_of_the_first_%27wall_formula%27_in_the_city_of_Utrecht_01.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/43/Picture_of_the_first_%27wall_formula%27_in_the_city_of_Utrecht_01.jpg/440px-Picture_of_the_first_%27wall_formula%27_in_the_city_of_Utrecht_01.jpg 2x" data-file-width="4032" data-file-height="3024" /></a><figcaption>Experiment by Buys Ballot (1845) depicted on a wall in Utrecht (2019)</figcaption></figure> <p>Doppler first proposed this effect in 1842 in his treatise "<i><a href="/wiki/%C3%9Cber_das_farbige_Licht_der_Doppelsterne_und_einiger_anderer_Gestirne_des_Himmels" class="mw-redirect" title="Über das farbige Licht der Doppelsterne und einiger anderer Gestirne des Himmels">Über das farbige Licht der Doppelsterne und einiger anderer Gestirne des Himmels</a></i>" (On the coloured light of the <a href="/wiki/Binary_stars" class="mw-redirect" title="Binary stars">binary stars</a> and some other stars of the heavens).<sup id="cite_ref-AlecEden_6-0" class="reference"><a href="#cite_note-AlecEden-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> The hypothesis was tested for sound waves by <a href="/wiki/C._H._D._Buys_Ballot" title="C. H. D. Buys Ballot">Buys Ballot</a> in 1845.<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>p 1<span class="cite-bracket">]</span></a></sup> He confirmed that the sound's <a href="/wiki/Pitch_(music)#Pitch_and_frequency" title="Pitch (music)">pitch</a> was higher than the emitted frequency when the sound source approached him, and lower than the emitted frequency when the sound source receded from him. <a href="/wiki/Hippolyte_Fizeau" title="Hippolyte Fizeau">Hippolyte Fizeau</a> discovered independently the same phenomenon on <a href="/wiki/Electromagnetic_wave" class="mw-redirect" title="Electromagnetic wave">electromagnetic waves</a> in 1848 (in France, the effect is sometimes called "effet Doppler-Fizeau" but that name was not adopted by the rest of the world as Fizeau's discovery was six years after Doppler's proposal).<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>p 2<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> In Britain, <a href="/wiki/John_Scott_Russell" title="John Scott Russell">John Scott Russell</a> made an experimental study of the Doppler effect (1848).<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>p 3<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="General">General</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Doppler_effect&action=edit&section=2" title="Edit section: General"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In classical physics, where the speeds of source and the receiver relative to the medium are lower than the speed of waves in the medium, the relationship between observed frequency <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/132e57acb643253e7810ee9702d9581f159a1c61" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.279ex; height:2.509ex;" alt="{\displaystyle f}"></span> and emitted frequency <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f_{\text{0}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>0</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f_{\text{0}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e8b6e44a30a297af5191bb54d912ad346b2734df" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.193ex; height:2.509ex;" alt="{\displaystyle f_{\text{0}}}"></span> is given by:<sup id="cite_ref-halliday_11-0" class="reference"><a href="#cite_note-halliday-11"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f=\left({\frac {c\pm v_{\text{r}}}{c\mp v_{\text{s}}}}\right)f_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mo>=</mo> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>c</mi> <mo>±</mo> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>r</mtext> </mrow> </msub> </mrow> <mrow> <mi>c</mi> <mo>∓</mo> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>s</mtext> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <msub> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f=\left({\frac {c\pm v_{\text{r}}}{c\mp v_{\text{s}}}}\right)f_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0ed997bc5f31f32413fa3827be77f0708f141915" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:17.07ex; height:6.176ex;" alt="{\displaystyle f=\left({\frac {c\pm v_{\text{r}}}{c\mp v_{\text{s}}}}\right)f_{0}}"></span> where </p> <ul><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle c}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>c</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/86a67b81c2de995bd608d5b2df50cd8cd7d92455" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.007ex; height:1.676ex;" alt="{\displaystyle c}"></span> is the propagation speed of waves in the medium;</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v_{\text{r}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>r</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v_{\text{r}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b732ef992c8ed9e1a6176f8f75fb8696df730d95" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.004ex; height:2.009ex;" alt="{\displaystyle v_{\text{r}}}"></span> is the speed of the receiver relative to the medium. In the formula, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v_{\text{r}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>r</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v_{\text{r}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b732ef992c8ed9e1a6176f8f75fb8696df730d95" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.004ex; height:2.009ex;" alt="{\displaystyle v_{\text{r}}}"></span> is added to <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle c}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>c</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/86a67b81c2de995bd608d5b2df50cd8cd7d92455" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.007ex; height:1.676ex;" alt="{\displaystyle c}"></span> if the receiver is moving towards the source, subtracted if the receiver is moving away from the source;</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v_{\text{s}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>s</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v_{\text{s}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b967b0fadf0e61501f222904f77e4f0bd87e67b9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.008ex; height:2.009ex;" alt="{\displaystyle v_{\text{s}}}"></span> is the speed of the source relative to the medium. <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v_{\text{s}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>s</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v_{\text{s}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b967b0fadf0e61501f222904f77e4f0bd87e67b9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.008ex; height:2.009ex;" alt="{\displaystyle v_{\text{s}}}"></span> is subtracted from <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle c}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>c</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/86a67b81c2de995bd608d5b2df50cd8cd7d92455" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.007ex; height:1.676ex;" alt="{\displaystyle c}"></span> if the source is moving towards the receiver, added if the source is moving away from the receiver.</li></ul> <p>Note this relationship predicts that the frequency will decrease if either source or receiver is moving away from the other. </p><p>Equivalently, under the assumption that the source is either directly approaching or receding from the observer: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {f}{v_{wr}}}={\frac {f_{0}}{v_{ws}}}={\frac {1}{\lambda }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>f</mi> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>w</mi> <mi>r</mi> </mrow> </msub> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>w</mi> <mi>s</mi> </mrow> </msub> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>λ</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {f}{v_{wr}}}={\frac {f_{0}}{v_{ws}}}={\frac {1}{\lambda }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2bbe54874e2cefc44a1e8857abbb73d9ccf31ba8" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:16.646ex; height:5.676ex;" alt="{\displaystyle {\frac {f}{v_{wr}}}={\frac {f_{0}}{v_{ws}}}={\frac {1}{\lambda }}}"></span> where </p> <ul><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v_{wr}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>w</mi> <mi>r</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v_{wr}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e5be0ac8d5796cc3d70eea6d3a578ba7fb2325e1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.278ex; height:2.009ex;" alt="{\displaystyle v_{wr}}"></span> is the wave's speed relative to the receiver;</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v_{ws}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>w</mi> <mi>s</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v_{ws}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8f804ddccd92171c60bef11146d8872bcce61037" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.308ex; height:2.009ex;" alt="{\displaystyle v_{ws}}"></span> is the wave's speed relative to the source;</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \lambda }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>λ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lambda }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b43d0ea3c9c025af1be9128e62a18fa74bedda2a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.355ex; height:2.176ex;" alt="{\displaystyle \lambda }"></span> is the wavelength.</li></ul> <p>If the source approaches the observer at an angle (but still with a constant speed), the observed frequency that is first heard is higher than the object's emitted frequency. Thereafter, there is a <a href="/wiki/Monotonic" class="mw-redirect" title="Monotonic">monotonic</a> decrease in the observed frequency as it gets closer to the observer, through equality when it is coming from a direction perpendicular to the relative motion (and was emitted at the point of closest approach; but when the wave is received, the source and observer will no longer be at their closest), and a continued monotonic decrease as it recedes from the observer. When the observer is very close to the path of the object, the transition from high to low frequency is very abrupt. When the observer is far from the path of the object, the transition from high to low frequency is gradual. </p><p>If the speeds <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v_{\text{s}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>s</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v_{\text{s}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b967b0fadf0e61501f222904f77e4f0bd87e67b9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.008ex; height:2.009ex;" alt="{\displaystyle v_{\text{s}}}"></span> and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v_{\text{r}}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>r</mtext> </mrow> </msub> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v_{\text{r}}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/42a3bd83cadb09f9c7b668486adba362d67098a0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.392ex; height:2.009ex;" alt="{\displaystyle v_{\text{r}}\,}"></span> are small compared to the speed of the wave, the relationship between observed frequency <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/132e57acb643253e7810ee9702d9581f159a1c61" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.279ex; height:2.509ex;" alt="{\displaystyle f}"></span> and emitted frequency <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f_{\text{0}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>0</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f_{\text{0}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e8b6e44a30a297af5191bb54d912ad346b2734df" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.193ex; height:2.509ex;" alt="{\displaystyle f_{\text{0}}}"></span> is approximately<sup id="cite_ref-halliday_11-1" class="reference"><a href="#cite_note-halliday-11"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> </p> <table> <tbody><tr> <th>Observed frequency</th> <th>Change in frequency </th></tr> <tr> <td width="70%"><div class="center" style="width:auto; margin-left:auto; margin-right:auto;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f=\left(1+{\frac {\Delta v}{c}}\right)f_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mo>=</mo> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">Δ</mi> <mi>v</mi> </mrow> <mi>c</mi> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> <msub> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f=\left(1+{\frac {\Delta v}{c}}\right)f_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/40a01dd1044f4fd5da9e006725e25fe2f3eb7f32" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:18.281ex; height:6.176ex;" alt="{\displaystyle f=\left(1+{\frac {\Delta v}{c}}\right)f_{0}}"></span></div></td> <td><div class="center" style="width:auto; margin-left:auto; margin-right:auto;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta f={\frac {\Delta v}{c}}f_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>f</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">Δ</mi> <mi>v</mi> </mrow> <mi>c</mi> </mfrac> </mrow> <msub> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta f={\frac {\Delta v}{c}}f_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5c849ba0e7fa8bb8c8239af2a7e5429c25df38e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:12.406ex; height:5.343ex;" alt="{\displaystyle \Delta f={\frac {\Delta v}{c}}f_{0}}"></span></div> </td></tr></tbody></table> <p>where </p> <ul><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta f=f-f_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>f</mi> <mo>=</mo> <mi>f</mi> <mo>−</mo> <msub> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta f=f-f_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/78f9fc709af6e3c21b614a13482244f5379b0663" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:12.625ex; height:2.509ex;" alt="{\displaystyle \Delta f=f-f_{0}}"></span></li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta v=-(v_{\text{r}}-v_{\text{s}})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>v</mi> <mo>=</mo> <mo>−</mo> <mo stretchy="false">(</mo> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>r</mtext> </mrow> </msub> <mo>−</mo> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>s</mtext> </mrow> </msub> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta v=-(v_{\text{r}}-v_{\text{s}})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/af43c7c306a6d443a8c9142ade0a200da8481ed1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:16.632ex; height:2.843ex;" alt="{\displaystyle \Delta v=-(v_{\text{r}}-v_{\text{s}})}"></span> is the opposite of the relative speed of the receiver with respect to the source: it is positive when the source and the receiver are moving towards each other.</li></ul> <style data-mw-deduplicate="TemplateStyles:r1174254338">.mw-parser-output .math_proof{border:thin solid #aaa;margin:1em 2em;padding:0.5em 1em 0.4em}@media(max-width:500px){.mw-parser-output .math_proof{margin:1em 0;padding:0.5em 0.5em 0.4em}}</style><div class="math_proof" style=""><strong>Proof</strong> <p>Given <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f=\left({\frac {c+v_{\text{r}}}{c+v_{\text{s}}}}\right)f_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mo>=</mo> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>c</mi> <mo>+</mo> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>r</mtext> </mrow> </msub> </mrow> <mrow> <mi>c</mi> <mo>+</mo> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>s</mtext> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <msub> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f=\left({\frac {c+v_{\text{r}}}{c+v_{\text{s}}}}\right)f_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/edefa636d4d33ac28088c5548038ed30483590aa" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:17.07ex; height:6.176ex;" alt="{\displaystyle f=\left({\frac {c+v_{\text{r}}}{c+v_{\text{s}}}}\right)f_{0}}"></span> </p><p>we divide for <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle c}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>c</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/86a67b81c2de995bd608d5b2df50cd8cd7d92455" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.007ex; height:1.676ex;" alt="{\displaystyle c}"></span> <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f=\left({\frac {1+{\frac {v_{\text{r}}}{c}}}{1+{\frac {v_{\text{s}}}{c}}}}\right)f_{0}=\left(1+{\frac {v_{\text{r}}}{c}}\right)\left({\frac {1}{1+{\frac {v_{\text{s}}}{c}}}}\right)f_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mo>=</mo> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>1</mn> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>r</mtext> </mrow> </msub> <mi>c</mi> </mfrac> </mrow> </mrow> <mrow> <mn>1</mn> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>s</mtext> </mrow> </msub> <mi>c</mi> </mfrac> </mrow> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <msub> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>=</mo> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>r</mtext> </mrow> </msub> <mi>c</mi> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mn>1</mn> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>s</mtext> </mrow> </msub> <mi>c</mi> </mfrac> </mrow> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <msub> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f=\left({\frac {1+{\frac {v_{\text{r}}}{c}}}{1+{\frac {v_{\text{s}}}{c}}}}\right)f_{0}=\left(1+{\frac {v_{\text{r}}}{c}}\right)\left({\frac {1}{1+{\frac {v_{\text{s}}}{c}}}}\right)f_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/73c314262bb71568373d7fd349f9d2913bedfda2" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:44.331ex; height:7.509ex;" alt="{\displaystyle f=\left({\frac {1+{\frac {v_{\text{r}}}{c}}}{1+{\frac {v_{\text{s}}}{c}}}}\right)f_{0}=\left(1+{\frac {v_{\text{r}}}{c}}\right)\left({\frac {1}{1+{\frac {v_{\text{s}}}{c}}}}\right)f_{0}}"></span> </p><p>Since <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {v_{\text{s}}}{c}}\ll 1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>s</mtext> </mrow> </msub> <mi>c</mi> </mfrac> </mrow> <mo>≪</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {v_{\text{s}}}{c}}\ll 1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ef70119e7510573d25bdc49f23ee9753aaaeb8fd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:7.62ex; height:4.676ex;" alt="{\displaystyle {\frac {v_{\text{s}}}{c}}\ll 1}"></span> we can substitute using the <a href="/wiki/Taylor%27s_series" class="mw-redirect" title="Taylor's series">Taylor's series</a> expansion of <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {1}{1+x}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mn>1</mn> <mo>+</mo> <mi>x</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {1}{1+x}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0e7d2df86c30c3b4ead9fdb615774af8a731a69a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:6.169ex; height:5.343ex;" alt="{\displaystyle {\frac {1}{1+x}}}"></span> truncating all <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cf0bf28fd28f45d07e1ceb909ce333c18c558c93" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.384ex; height:2.676ex;" alt="{\displaystyle x^{2}}"></span> and higher terms: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {1}{1+{\frac {v_{\text{s}}}{c}}}}\approx 1-{\frac {v_{\text{s}}}{c}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mn>1</mn> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>s</mtext> </mrow> </msub> <mi>c</mi> </mfrac> </mrow> </mrow> </mfrac> </mrow> <mo>≈</mo> <mn>1</mn> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>s</mtext> </mrow> </msub> <mi>c</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {1}{1+{\frac {v_{\text{s}}}{c}}}}\approx 1-{\frac {v_{\text{s}}}{c}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4c8f217640d8d02a9ac0daffcfd081c4be5dbbbc" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:17.108ex; height:6.509ex;" alt="{\displaystyle {\frac {1}{1+{\frac {v_{\text{s}}}{c}}}}\approx 1-{\frac {v_{\text{s}}}{c}}}"></span> </p><p>When substituted in the last line, one gets: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left(1+{\frac {v_{\text{r}}}{c}}\right)\left(1-{\frac {v_{\text{s}}}{c}}\right)f_{0}=\left(1+{\frac {v_{\text{r}}}{c}}-{\frac {v_{\text{s}}}{c}}-{\frac {v_{\text{r}}v_{\text{s}}}{c^{2}}}\right)f_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>r</mtext> </mrow> </msub> <mi>c</mi> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>s</mtext> </mrow> </msub> <mi>c</mi> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> <msub> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>=</mo> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>r</mtext> </mrow> </msub> <mi>c</mi> </mfrac> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>s</mtext> </mrow> </msub> <mi>c</mi> </mfrac> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>r</mtext> </mrow> </msub> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>s</mtext> </mrow> </msub> </mrow> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> <msub> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left(1+{\frac {v_{\text{r}}}{c}}\right)\left(1-{\frac {v_{\text{s}}}{c}}\right)f_{0}=\left(1+{\frac {v_{\text{r}}}{c}}-{\frac {v_{\text{s}}}{c}}-{\frac {v_{\text{r}}v_{\text{s}}}{c^{2}}}\right)f_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e3ea196a3df645e9aba4374c0cab1ee7776951c6" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:51.526ex; height:6.176ex;" alt="{\displaystyle \left(1+{\frac {v_{\text{r}}}{c}}\right)\left(1-{\frac {v_{\text{s}}}{c}}\right)f_{0}=\left(1+{\frac {v_{\text{r}}}{c}}-{\frac {v_{\text{s}}}{c}}-{\frac {v_{\text{r}}v_{\text{s}}}{c^{2}}}\right)f_{0}}"></span> </p><p>For small <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v_{\text{s}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>s</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v_{\text{s}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b967b0fadf0e61501f222904f77e4f0bd87e67b9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.008ex; height:2.009ex;" alt="{\displaystyle v_{\text{s}}}"></span> and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v_{\text{r}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>r</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v_{\text{r}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b732ef992c8ed9e1a6176f8f75fb8696df730d95" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.004ex; height:2.009ex;" alt="{\displaystyle v_{\text{r}}}"></span>, the last term <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {v_{\text{r}}v_{\text{s}}}{c^{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>r</mtext> </mrow> </msub> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>s</mtext> </mrow> </msub> </mrow> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {v_{\text{r}}v_{\text{s}}}{c^{2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1f310769f794a8d0ef6897663fdff2fac9428833" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:4.848ex; height:5.009ex;" alt="{\displaystyle {\frac {v_{\text{r}}v_{\text{s}}}{c^{2}}}}"></span> becomes insignificant, hence: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left(1+{\frac {v_{\text{r}}-v_{\text{s}}}{c}}\right)f_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>r</mtext> </mrow> </msub> <mo>−</mo> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>s</mtext> </mrow> </msub> </mrow> <mi>c</mi> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> <msub> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left(1+{\frac {v_{\text{r}}-v_{\text{s}}}{c}}\right)f_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d6e876a96d70462807c92c616dca7229fbcf656e" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:17.693ex; height:6.176ex;" alt="{\displaystyle \left(1+{\frac {v_{\text{r}}-v_{\text{s}}}{c}}\right)f_{0}}"></span> </p> </div> <ul class="gallery mw-gallery-packed"> <li class="gallerybox" style="width: 254px"> <div class="thumb" style="width: 252px;"><span typeof="mw:File"><a href="/wiki/File:Dopplereffectstationary.gif" class="mw-file-description" title="Stationary sound source produces sound waves at a constant frequency f, and the wave-fronts propagate symmetrically away from the source at a constant speed c. The distance between wave-fronts is the wavelength. All observers will hear the same frequency, which will be equal to the actual frequency of the source where f = f0."><img alt="Stationary sound source produces sound waves at a constant frequency f, and the wave-fronts propagate symmetrically away from the source at a constant speed c. The distance between wave-fronts is the wavelength. All observers will hear the same frequency, which will be equal to the actual frequency of the source where f = f0." src="//upload.wikimedia.org/wikipedia/commons/e/e3/Dopplereffectstationary.gif" decoding="async" width="252" height="250" class="mw-file-element" data-file-width="300" data-file-height="298" /></a></span></div> <div class="gallerytext">Stationary sound source produces sound waves at a constant frequency <span class="texhtml"><i>f</i></span>, and the wave-fronts propagate symmetrically away from the source at a constant speed c. The distance between wave-fronts is the wavelength. All observers will hear the same frequency, which will be equal to the actual frequency of the source where <span class="texhtml"><i>f</i> = <i>f</i><sub>0</sub></span>.</div> </li> <li class="gallerybox" style="width: 254px"> <div class="thumb" style="width: 252px;"><span typeof="mw:File"><a href="/wiki/File:Dopplereffectsourcemovingrightatmach0.7.gif" class="mw-file-description" title="The same sound source is radiating sound waves at a constant frequency in the same medium. However, now the sound source is moving with a speed υs = 0.7 c. Since the source is moving, the centre of each new wavefront is now slightly displaced to the right. As a result, the wave-fronts begin to bunch up on the right side (in front of) and spread further apart on the left side (behind) of the source. An observer in front of the source will hear a higher frequency f = ⁠c + 0/c – 0.7c⁠ f0 = 3.33 f0 and an observer behind the source will hear a lower frequency f = ⁠c − 0/c + 0.7c⁠ f0 = 0.59 f0."><img alt="The same sound source is radiating sound waves at a constant frequency in the same medium. However, now the sound source is moving with a speed υs = 0.7 c. Since the source is moving, the centre of each new wavefront is now slightly displaced to the right. As a result, the wave-fronts begin to bunch up on the right side (in front of) and spread further apart on the left side (behind) of the source. An observer in front of the source will hear a higher frequency f = ⁠c + 0/c – 0.7c⁠ f0 = 3.33 f0 and an observer behind the source will hear a lower frequency f = ⁠c − 0/c + 0.7c⁠ f0 = 0.59 f0." src="//upload.wikimedia.org/wikipedia/commons/c/c9/Dopplereffectsourcemovingrightatmach0.7.gif" decoding="async" width="252" height="250" class="mw-file-element" data-file-width="300" data-file-height="298" /></a></span></div> <div class="gallerytext">The same sound source is <a href="/wiki/Radiating" class="mw-redirect" title="Radiating">radiating</a> sound waves at a constant frequency in the same medium. However, now the sound source is moving with a speed <span class="texhtml"><i>υ</i><sub>s</sub> = 0.7 <i>c</i></span>. Since the source is moving, the centre of each new <a href="/wiki/Wavefront" title="Wavefront">wavefront</a> is now slightly displaced to the right. As a result, the wave-fronts begin to bunch up on the right side (in front of) and spread further apart on the left side (behind) of the source. An observer in front of the source will hear a higher frequency <span class="texhtml"><i>f</i> = <style data-mw-deduplicate="TemplateStyles:r1214402035">.mw-parser-output .sfrac{white-space:nowrap}.mw-parser-output .sfrac.tion,.mw-parser-output .sfrac .tion{display:inline-block;vertical-align:-0.5em;font-size:85%;text-align:center}.mw-parser-output .sfrac .num{display:block;line-height:1em;margin:0.0em 0.1em;border-bottom:1px solid}.mw-parser-output .sfrac .den{display:block;line-height:1em;margin:0.1em 0.1em}.mw-parser-output .sr-only{border:0;clip:rect(0,0,0,0);clip-path:polygon(0px 0px,0px 0px,0px 0px);height:1px;margin:-1px;overflow:hidden;padding:0;position:absolute;width:1px}</style><span class="sfrac">⁠<span class="tion"><span class="num"><i>c</i> + 0</span><span class="sr-only">/</span><span class="den"><i>c</i> – 0.7<i>c</i></span></span>⁠</span> <i>f</i><sub>0</sub> = 3.33 <i>f</i><sub>0</sub></span> and an observer behind the source will hear a lower frequency <span class="texhtml"><i>f</i> = <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num"><i>c</i> − 0</span><span class="sr-only">/</span><span class="den"><i>c</i> + 0.7<i>c</i></span></span>⁠</span> <i>f</i><sub>0</sub> = 0.59 <i>f</i><sub>0</sub></span>.</div> </li> <li class="gallerybox" style="width: 254.66666666667px"> <div class="thumb" style="width: 252.66666666667px;"><span typeof="mw:File"><a href="/wiki/File:Dopplereffectsourcemovingrightatmach1.0.gif" class="mw-file-description" title="Now the source is moving at the speed of sound in the medium (υs = c). The wave fronts in front of the source are now all bunched up at the same point. As a result, an observer in front of the source will detect nothing until the source arrives and an observer behind the source will hear a lower frequency f = ⁠c – 0/c + c⁠ f0 = 0.5 f0."><img alt="Now the source is moving at the speed of sound in the medium (υs = c). The wave fronts in front of the source are now all bunched up at the same point. As a result, an observer in front of the source will detect nothing until the source arrives and an observer behind the source will hear a lower frequency f = ⁠c – 0/c + c⁠ f0 = 0.5 f0." src="//upload.wikimedia.org/wikipedia/commons/d/d1/Dopplereffectsourcemovingrightatmach1.0.gif" decoding="async" width="253" height="250" class="mw-file-element" data-file-width="301" data-file-height="298" /></a></span></div> <div class="gallerytext">Now the source is moving at the speed of sound in the medium (<span class="texhtml"><i>υ</i><sub>s</sub> = <i>c</i></span>). The wave fronts in front of the source are now all bunched up at the same point. As a result, an observer in front of the source will detect nothing until the source arrives and an observer behind the source will hear a lower frequency <span class="texhtml"><i>f</i> = <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num"><i>c</i> – 0</span><span class="sr-only">/</span><span class="den"><i>c</i> + <i>c</i></span></span>⁠</span> <i>f</i><sub>0</sub> = 0.5 <i>f</i><sub>0</sub></span>.</div> </li> <li class="gallerybox" style="width: 254.66666666667px"> <div class="thumb" style="width: 252.66666666667px;"><span typeof="mw:File"><a href="/wiki/File:Dopplereffectsourcemovingrightatmach1.4.gif" class="mw-file-description" title="The sound source has now surpassed the speed of sound in the medium, and is traveling at 1.4 c. Since the source is moving faster than the sound waves it creates, it actually leads the advancing wavefront. The sound source will pass by a stationary observer before the observer hears the sound. As a result, an observer in front of the source will detect nothing and an observer behind the source will hear a lower frequency f = ⁠c – 0/c + 1.4c⁠ f0 = 0.42 f0."><img alt="The sound source has now surpassed the speed of sound in the medium, and is traveling at 1.4 c. Since the source is moving faster than the sound waves it creates, it actually leads the advancing wavefront. The sound source will pass by a stationary observer before the observer hears the sound. As a result, an observer in front of the source will detect nothing and an observer behind the source will hear a lower frequency f = ⁠c – 0/c + 1.4c⁠ f0 = 0.42 f0." src="//upload.wikimedia.org/wikipedia/commons/e/e4/Dopplereffectsourcemovingrightatmach1.4.gif" decoding="async" width="253" height="250" class="mw-file-element" data-file-width="301" data-file-height="298" /></a></span></div> <div class="gallerytext">The sound source has now surpassed the speed of sound in the medium, and is traveling at 1.4 <i>c</i>. Since the source is moving faster than the sound waves it creates, it actually leads the advancing wavefront. The sound source will pass by a stationary observer before the observer hears the sound. As a result, an observer in front of the source will detect nothing and an observer behind the source will hear a lower frequency <span class="texhtml"><i>f</i> = <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num"><i>c</i> – 0</span><span class="sr-only">/</span><span class="den"><i>c</i> + 1.4<i>c</i></span></span>⁠</span> <i>f</i><sub>0</sub> = 0.42 <i>f</i><sub>0</sub></span>.</div> </li> </ul> <div class="mw-heading mw-heading2"><h2 id="Consequences">Consequences</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Doppler_effect&action=edit&section=3" title="Edit section: Consequences"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Assuming a stationary observer and a wave source moving towards the observer at (or exceeding) the speed of the wave, the Doppler equation predicts an infinite (or negative) frequency as from the observer's perspective. Thus, the Doppler equation is inapplicable for such cases. If the wave is a sound wave and the sound source is moving faster than the speed of sound, the resulting <a href="/wiki/Shock_wave" title="Shock wave">shock wave</a> creates a <a href="/wiki/Sonic_boom" title="Sonic boom">sonic boom</a>. </p><p><a href="/wiki/John_William_Strutt,_3rd_Baron_Rayleigh" title="John William Strutt, 3rd Baron Rayleigh">Lord Rayleigh</a> predicted the following effect in his classic book on sound: if the observer were moving from the (stationary) source at twice the speed of sound, a musical piece <i>previously</i> emitted by that source would be heard in correct tempo and pitch, but as if played <i>backwards</i>.<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Applications">Applications</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Doppler_effect&action=edit&section=4" title="Edit section: Applications"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Sirens">Sirens</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Doppler_effect&action=edit&section=5" title="Edit section: Sirens"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><span><video id="mwe_player_1" poster="//upload.wikimedia.org/wikipedia/commons/thumb/0/07/Juli_2016_-_Spoedtransport%2C_Huisarts%2C_Brandweer%2C_Politie_en_Ambulances_met_spoed_in_Rotterdam_-451.webm/220px-seek%3D434-Juli_2016_-_Spoedtransport%2C_Huisarts%2C_Brandweer%2C_Politie_en_Ambulances_met_spoed_in_Rotterdam_-451.webm.jpg" controls="" preload="none" data-mw-tmh="" class="mw-file-element" width="220" height="124" data-durationhint="720" data-mwtitle="Juli_2016_-_Spoedtransport,_Huisarts,_Brandweer,_Politie_en_Ambulances_met_spoed_in_Rotterdam_-451.webm" data-mwprovider="wikimediacommons" resource="/wiki/File:Juli_2016_-_Spoedtransport,_Huisarts,_Brandweer,_Politie_en_Ambulances_met_spoed_in_Rotterdam_-451.webm"><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/0/07/Juli_2016_-_Spoedtransport%2C_Huisarts%2C_Brandweer%2C_Politie_en_Ambulances_met_spoed_in_Rotterdam_-451.webm/Juli_2016_-_Spoedtransport%2C_Huisarts%2C_Brandweer%2C_Politie_en_Ambulances_met_spoed_in_Rotterdam_-451.webm.480p.vp9.webm#t=00:07:14,00:08:30" type="video/webm; codecs="vp9, opus"" data-transcodekey="480p.vp9.webm" data-width="854" data-height="480" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/0/07/Juli_2016_-_Spoedtransport%2C_Huisarts%2C_Brandweer%2C_Politie_en_Ambulances_met_spoed_in_Rotterdam_-451.webm/Juli_2016_-_Spoedtransport%2C_Huisarts%2C_Brandweer%2C_Politie_en_Ambulances_met_spoed_in_Rotterdam_-451.webm.720p.vp9.webm#t=00:07:14,00:08:30" type="video/webm; codecs="vp9, opus"" data-transcodekey="720p.vp9.webm" data-width="1280" data-height="720" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/0/07/Juli_2016_-_Spoedtransport%2C_Huisarts%2C_Brandweer%2C_Politie_en_Ambulances_met_spoed_in_Rotterdam_-451.webm/Juli_2016_-_Spoedtransport%2C_Huisarts%2C_Brandweer%2C_Politie_en_Ambulances_met_spoed_in_Rotterdam_-451.webm.1080p.vp9.webm#t=00:07:14,00:08:30" type="video/webm; codecs="vp9, opus"" data-transcodekey="1080p.vp9.webm" data-width="1920" data-height="1080" /><source src="//upload.wikimedia.org/wikipedia/commons/0/07/Juli_2016_-_Spoedtransport%2C_Huisarts%2C_Brandweer%2C_Politie_en_Ambulances_met_spoed_in_Rotterdam_-451.webm#t=00:07:14,00:08:30" type="video/webm; codecs="vp8, vorbis"" data-width="1920" data-height="1080" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/0/07/Juli_2016_-_Spoedtransport%2C_Huisarts%2C_Brandweer%2C_Politie_en_Ambulances_met_spoed_in_Rotterdam_-451.webm/Juli_2016_-_Spoedtransport%2C_Huisarts%2C_Brandweer%2C_Politie_en_Ambulances_met_spoed_in_Rotterdam_-451.webm.144p.mjpeg.mov#t=00:07:14,00:08:30" type="video/quicktime" data-transcodekey="144p.mjpeg.mov" data-width="256" data-height="144" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/0/07/Juli_2016_-_Spoedtransport%2C_Huisarts%2C_Brandweer%2C_Politie_en_Ambulances_met_spoed_in_Rotterdam_-451.webm/Juli_2016_-_Spoedtransport%2C_Huisarts%2C_Brandweer%2C_Politie_en_Ambulances_met_spoed_in_Rotterdam_-451.webm.240p.vp9.webm#t=00:07:14,00:08:30" type="video/webm; codecs="vp9, opus"" data-transcodekey="240p.vp9.webm" data-width="426" data-height="240" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/0/07/Juli_2016_-_Spoedtransport%2C_Huisarts%2C_Brandweer%2C_Politie_en_Ambulances_met_spoed_in_Rotterdam_-451.webm/Juli_2016_-_Spoedtransport%2C_Huisarts%2C_Brandweer%2C_Politie_en_Ambulances_met_spoed_in_Rotterdam_-451.webm.360p.webm#t=00:07:14,00:08:30" type="video/webm; codecs="vp8, vorbis"" data-transcodekey="360p.webm" data-width="640" data-height="360" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/0/07/Juli_2016_-_Spoedtransport%2C_Huisarts%2C_Brandweer%2C_Politie_en_Ambulances_met_spoed_in_Rotterdam_-451.webm/Juli_2016_-_Spoedtransport%2C_Huisarts%2C_Brandweer%2C_Politie_en_Ambulances_met_spoed_in_Rotterdam_-451.webm.360p.vp9.webm#t=00:07:14,00:08:30" type="video/webm; codecs="vp9, opus"" data-transcodekey="360p.vp9.webm" data-width="640" data-height="360" /></video></span><figcaption>Sirens on passing emergency vehicles.</figcaption></figure> <p>A <a href="/wiki/Siren_(alarm)" title="Siren (alarm)">siren</a> on a passing <a href="/wiki/Emergency_vehicle" title="Emergency vehicle">emergency vehicle</a> will start out higher than its stationary pitch, slide down as it passes, and continue lower than its stationary pitch as it recedes from the observer. Astronomer <a href="/wiki/John_Dobson_(astronomer)" class="mw-redirect" title="John Dobson (astronomer)">John Dobson</a> explained the effect thus: </p> <style data-mw-deduplicate="TemplateStyles:r1244412712">.mw-parser-output .templatequote{overflow:hidden;margin:1em 0;padding:0 32px}.mw-parser-output .templatequotecite{line-height:1.5em;text-align:left;margin-top:0}@media(min-width:500px){.mw-parser-output .templatequotecite{padding-left:1.6em}}</style><blockquote class="templatequote"><p>The reason the siren slides is because it doesn't hit you.</p></blockquote> <p>In other words, if the siren approached the observer directly, the pitch would remain constant, at a higher than stationary pitch, until the vehicle hit him, and then immediately jump to a new lower pitch. Because the vehicle passes by the observer, the radial speed does not remain constant, but instead varies as a function of the angle between his line of sight and the siren's velocity: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v_{\text{radial}}=v_{\text{s}}\cos(\theta )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>radial</mtext> </mrow> </msub> <mo>=</mo> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>s</mtext> </mrow> </msub> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>θ</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v_{\text{radial}}=v_{\text{s}}\cos(\theta )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d3dd3ba6acafdaea1cffac5954dd80feffa1656b" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:16.981ex; height:2.843ex;" alt="{\displaystyle v_{\text{radial}}=v_{\text{s}}\cos(\theta )}"></span> where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \theta }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>θ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \theta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6e5ab2664b422d53eb0c7df3b87e1360d75ad9af" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.09ex; height:2.176ex;" alt="{\displaystyle \theta }"></span> is the angle between the object's forward velocity and the line of sight from the object to the observer. </p> <div class="mw-heading mw-heading3"><h3 id="Astronomy">Astronomy</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Doppler_effect&action=edit&section=6" title="Edit section: Astronomy"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Relativistic_Doppler_effect" title="Relativistic Doppler effect">Relativistic Doppler effect</a></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Redshift.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6a/Redshift.svg/170px-Redshift.svg.png" decoding="async" width="170" height="301" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6a/Redshift.svg/255px-Redshift.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6a/Redshift.svg/340px-Redshift.svg.png 2x" data-file-width="300" data-file-height="532" /></a><figcaption><a href="/wiki/Redshift" title="Redshift">Redshift</a> of <a href="/wiki/Spectral_line" title="Spectral line">spectral lines</a> in the <a href="/wiki/Optical_spectrum" class="mw-redirect" title="Optical spectrum">optical spectrum</a> of a supercluster of distant galaxies (right), as compared to that of the Sun (left)</figcaption></figure> <p>The <a href="/wiki/Relativistic_Doppler_effect" title="Relativistic Doppler effect">Doppler effect for electromagnetic waves</a> such as light is of widespread use in <a href="/wiki/Astronomy" title="Astronomy">astronomy</a> to measure the speed at which <a href="/wiki/Star" title="Star">stars</a> and <a href="/wiki/Galaxy" title="Galaxy">galaxies</a> are approaching or receding from us, resulting in so called <a href="/wiki/Blueshift" class="mw-redirect" title="Blueshift">blueshift</a> or <a href="/wiki/Redshift" title="Redshift">redshift</a>, respectively. This may be used to detect if an apparently single star is, in reality, a close <a href="/wiki/Binary_star" title="Binary star">binary</a>, to measure the rotational speed of stars and galaxies, or to <a href="/wiki/Doppler_spectroscopy" title="Doppler spectroscopy">detect exoplanets</a>. This effect typically happens on a very small scale; there would not be a noticeable difference in visible light to the unaided eye.<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> The use of the Doppler effect in astronomy depends on knowledge of precise frequencies of <a href="/wiki/Spectral_line" title="Spectral line">discrete lines</a> in the <a href="/wiki/Electromagnetic_spectroscopy" class="mw-redirect" title="Electromagnetic spectroscopy">spectra</a> of stars. </p><p>Among the <a href="/wiki/List_of_nearest_stars" title="List of nearest stars">nearby stars</a>, the largest <a href="/wiki/Radial_velocities" class="mw-redirect" title="Radial velocities">radial velocities</a> with respect to the <a href="/wiki/Sun" title="Sun">Sun</a> are +308 km/s (<a href="/w/index.php?title=BD-15%C2%B04041&action=edit&redlink=1" class="new" title="BD-15°4041 (page does not exist)">BD-15°4041</a>, also known as LHS 52, 81.7 light-years away) and −260 km/s (<a href="/w/index.php?title=Woolley_9722&action=edit&redlink=1" class="new" title="Woolley 9722 (page does not exist)">Woolley 9722</a>, also known as Wolf 1106 and LHS 64, 78.2 light-years away). Positive radial speed means the star is receding from the Sun, negative that it is approaching. </p><p>Redshift is also used to measure the <a href="/wiki/Redshift#Expansion_of_space" title="Redshift">expansion of the universe</a>. It is sometimes claimed that this is not truly a Doppler effect but instead arises from the expansion of space.<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> However, this picture can be misleading because the expansion of space is only a mathematical convention, corresponding to a choice of <a href="/wiki/Coordinate_conditions" title="Coordinate conditions">coordinates</a>.<sup id="cite_ref-Peacock_15-0" class="reference"><a href="#cite_note-Peacock-15"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> The most natural interpretation of the cosmological redshift is that it is indeed a Doppler shift.<sup id="cite_ref-Hogg_16-0" class="reference"><a href="#cite_note-Hogg-16"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> </p><p>Distant galaxies also exhibit <a href="/wiki/Peculiar_motion" class="mw-redirect" title="Peculiar motion">peculiar motion</a> distinct from their cosmological recession speeds. If redshifts are used to determine distances in accordance with <a href="/wiki/Hubble%27s_law" title="Hubble's law">Hubble's law</a>, then these peculiar motions give rise to <a href="/wiki/Redshift-space_distortions" title="Redshift-space distortions">redshift-space distortions</a>.<sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Radar">Radar</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Doppler_effect&action=edit&section=7" title="Edit section: Radar"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Doppler_radar" title="Doppler radar">Doppler radar</a></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Radar_gun.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/cc/Radar_gun.jpg/220px-Radar_gun.jpg" decoding="async" width="220" height="143" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/cc/Radar_gun.jpg/330px-Radar_gun.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/cc/Radar_gun.jpg/440px-Radar_gun.jpg 2x" data-file-width="500" data-file-height="326" /></a><figcaption>U.S. Military Police using a <a href="/wiki/Radar_gun" class="mw-redirect" title="Radar gun">radar gun</a>, an application of Doppler radar, to catch speeding violators.</figcaption></figure> <p>The Doppler effect is used in some types of <a href="/wiki/Radar" title="Radar">radar</a>, to measure the velocity of detected objects. A radar beam is fired at a moving target – e.g. a motor car, as police use radar to detect speeding motorists – as it approaches or recedes from the radar source. Each successive radar wave has to travel farther to reach the car, before being reflected and re-detected near the source. As each wave has to move farther, the gap between each wave increases, increasing the wavelength. In some situations, the radar beam is fired at the moving car as it approaches, in which case each successive wave travels a lesser distance, decreasing the wavelength. In either situation, calculations from the Doppler effect accurately determine the car's speed. Moreover, the <a href="/wiki/Proximity_fuze" title="Proximity fuze">proximity fuze</a>, developed during World War II, relies upon Doppler radar to detonate explosives at the correct time, height, distance, etc.<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (December 2009)">citation needed</span></a></i>]</sup> </p><p>Because the Doppler shift affects the wave incident upon the target as well as the wave reflected back to the radar, the change in frequency observed by a radar due to a target moving at relative speed <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta v}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>v</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta v}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e18b43e4225eeaafeeb25aefc4ee90bd86f004dc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.063ex; height:2.176ex;" alt="{\displaystyle \Delta v}"></span> is twice that from the same target emitting a wave:<sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup> <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta f={\frac {2\Delta v}{c}}f_{0}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>f</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>2</mn> <mi mathvariant="normal">Δ</mi> <mi>v</mi> </mrow> <mi>c</mi> </mfrac> </mrow> <msub> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta f={\frac {2\Delta v}{c}}f_{0}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/85234145d57ca31d9c3b5afd160a9794c9799121" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:14.215ex; height:5.343ex;" alt="{\displaystyle \Delta f={\frac {2\Delta v}{c}}f_{0}.}"></span> </p> <div class="mw-heading mw-heading3"><h3 id="Medical">Medical</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Doppler_effect&action=edit&section=8" title="Edit section: Medical"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Doppler_ultrasonography" title="Doppler ultrasonography">Doppler ultrasonography</a></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:CarotidDoppler1.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/64/CarotidDoppler1.jpg/170px-CarotidDoppler1.jpg" decoding="async" width="170" height="269" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/64/CarotidDoppler1.jpg/255px-CarotidDoppler1.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/64/CarotidDoppler1.jpg/340px-CarotidDoppler1.jpg 2x" data-file-width="1608" data-file-height="2544" /></a><figcaption>Colour flow ultrasonography (Doppler) of a <a href="/wiki/Carotid_artery" title="Carotid artery">carotid artery</a> – scanner and screen</figcaption></figure> <p>An <a href="/wiki/Echocardiogram" class="mw-redirect" title="Echocardiogram">echocardiogram</a> can, within certain limits, produce an accurate assessment of the direction of blood flow and the velocity of blood and cardiac tissue at any arbitrary point using the Doppler effect. One of the limitations is that the <a href="/wiki/Ultrasound" title="Ultrasound">ultrasound</a> beam should be as parallel to the blood flow as possible. Velocity measurements allow assessment of cardiac valve areas and function, abnormal communications between the left and right side of the heart, leaking of blood through the valves (valvular regurgitation), and calculation of the <a href="/wiki/Cardiac_output" title="Cardiac output">cardiac output</a>. <a href="/wiki/Contrast-enhanced_ultrasound" title="Contrast-enhanced ultrasound">Contrast-enhanced ultrasound</a> using gas-filled microbubble contrast media can be used to improve velocity or other flow-related medical measurements.<sup id="cite_ref-19" class="reference"><a href="#cite_note-19"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-20" class="reference"><a href="#cite_note-20"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> </p><p>Although "Doppler" has become synonymous with "velocity measurement" in medical imaging, in many cases it is not the frequency shift (Doppler shift) of the received signal that is measured, but the phase shift (<i>when</i> the received signal arrives).<sup id="cite_ref-21" class="reference"><a href="#cite_note-21"><span class="cite-bracket">[</span>p 4<span class="cite-bracket">]</span></a></sup> </p><p>Velocity measurements of blood flow are also used in other fields of <a href="/wiki/Medical_ultrasonography" class="mw-redirect" title="Medical ultrasonography">medical ultrasonography</a>, such as <a href="/wiki/Obstetric_ultrasonography" title="Obstetric ultrasonography">obstetric ultrasonography</a> and <a href="/wiki/Neurology" title="Neurology">neurology</a>. Velocity measurement of blood flow in arteries and veins based on Doppler effect is an effective tool for diagnosis of vascular problems like <a href="/wiki/Stenosis" title="Stenosis">stenosis</a>.<sup id="cite_ref-22" class="reference"><a href="#cite_note-22"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Flow_measurement">Flow measurement</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Doppler_effect&action=edit&section=9" title="Edit section: Flow measurement"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Instruments such as the <a href="/wiki/Laser_Doppler_velocimetry" title="Laser Doppler velocimetry">laser Doppler velocimeter</a> (LDV), and <a href="/wiki/Acoustic_Doppler_velocimetry" title="Acoustic Doppler velocimetry">acoustic Doppler velocimeter</a> (ADV) have been developed to measure velocities in a fluid flow. The LDV emits a light beam and the ADV emits an ultrasonic acoustic burst, and measure the Doppler shift in wavelengths of reflections from particles moving with the flow. The actual flow is computed as a function of the water velocity and phase. This technique allows non-intrusive flow measurements, at high precision and high frequency. </p> <div class="mw-heading mw-heading3"><h3 id="Velocity_profile_measurement">Velocity profile measurement</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Doppler_effect&action=edit&section=10" title="Edit section: Velocity profile measurement"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Developed originally for velocity measurements in medical applications (blood flow), Ultrasonic Doppler Velocimetry (UDV) can measure in real time complete velocity profile in almost any liquids containing particles in suspension such as dust, gas bubbles, emulsions. Flows can be pulsating, oscillating, laminar or turbulent, stationary or transient. This technique is fully non-invasive. </p> <div class="mw-heading mw-heading3"><h3 id="Satellites">Satellites</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Doppler_effect&action=edit&section=11" title="Edit section: Satellites"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <table style="margin: 0 auto;"> <tbody><tr> <td><figure typeof="mw:File/Thumb"><a href="/wiki/File:SatDoppler.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a6/SatDoppler.png/300px-SatDoppler.png" decoding="async" width="300" height="225" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a6/SatDoppler.png/450px-SatDoppler.png 1.5x, //upload.wikimedia.org/wikipedia/commons/a/a6/SatDoppler.png 2x" data-file-width="561" data-file-height="420" /></a><figcaption>Possible Doppler shifts in dependence of the elevation angle (<a href="/wiki/Low_Earth_orbit" title="Low Earth orbit">LEO</a>: orbit altitude <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle h}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>h</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle h}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b26be3e694314bc90c3215047e4a2010c6ee184a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.339ex; height:2.176ex;" alt="{\displaystyle h}"></span> = 750 km). Fixed ground station.<sup id="cite_ref-23" class="reference"><a href="#cite_note-23"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup></figcaption></figure> </td> <td><figure typeof="mw:File/Thumb"><a href="/wiki/File:DopplerSatScheme.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e4/DopplerSatScheme.png/300px-DopplerSatScheme.png" decoding="async" width="300" height="197" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e4/DopplerSatScheme.png/450px-DopplerSatScheme.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e4/DopplerSatScheme.png/600px-DopplerSatScheme.png 2x" data-file-width="948" data-file-height="622" /></a><figcaption>Geometry for Doppler effects. Variables: <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\vec {v}}_{\text{mob}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>v</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext>mob</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {v}}_{\text{mob}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/53ab515c26223bba47d5adc7a11a17044f4b390e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.512ex; height:2.676ex;" alt="{\displaystyle {\vec {v}}_{\text{mob}}}"></span> is the velocity of the mobile station, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\vec {v}}_{\text{Sat}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>v</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext>Sat</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {v}}_{\text{Sat}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a6a7e65f90c9d35258a521f8e00005ad5ed0da53" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.783ex; height:2.676ex;" alt="{\displaystyle {\vec {v}}_{\text{Sat}}}"></span> is the velocity of the satellite, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\vec {v}}_{\text{rel,sat}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>v</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext>rel,sat</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {v}}_{\text{rel,sat}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3244bc992650c9db18f3d9a0963869efe7e4a0dc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:5.807ex; height:3.009ex;" alt="{\displaystyle {\vec {v}}_{\text{rel,sat}}}"></span> is the relative velocity of the satellite, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \phi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ϕ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \phi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/72b1f30316670aee6270a28334bdf4f5072cdde4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.385ex; height:2.509ex;" alt="{\displaystyle \phi }"></span> is the elevation angle of the satellite and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \theta }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>θ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \theta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6e5ab2664b422d53eb0c7df3b87e1360d75ad9af" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.09ex; height:2.176ex;" alt="{\displaystyle \theta }"></span> is the driving direction with respect to the satellite.</figcaption></figure> </td> <td><figure typeof="mw:File/Thumb"><a href="/wiki/File:SatDopplerSpectrum.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e3/SatDopplerSpectrum.png/300px-SatDopplerSpectrum.png" decoding="async" width="300" height="226" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e3/SatDopplerSpectrum.png/450px-SatDopplerSpectrum.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e3/SatDopplerSpectrum.png/600px-SatDopplerSpectrum.png 2x" data-file-width="1042" data-file-height="786" /></a><figcaption>Doppler effect on the mobile channel. Variables: <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f_{c}={\frac {c}{\lambda _{\rm {c}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>c</mi> <msub> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">c</mi> </mrow> </mrow> </msub> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f_{c}={\frac {c}{\lambda _{\rm {c}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c1f51e5f4b504cd050b98a358a991bd91bb825af" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:8.336ex; height:5.176ex;" alt="{\displaystyle f_{c}={\frac {c}{\lambda _{\rm {c}}}}}"></span> is the carrier frequency, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f_{\rm {D,max}}={\frac {v_{\rm {mob}}}{\lambda _{\rm {c}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">D</mi> <mo>,</mo> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">x</mi> </mrow> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">o</mi> <mi mathvariant="normal">b</mi> </mrow> </mrow> </msub> <msub> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">c</mi> </mrow> </mrow> </msub> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f_{\rm {D,max}}={\frac {v_{\rm {mob}}}{\lambda _{\rm {c}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5dffca64f0160859fba94625ac45b55adc5ed8fa" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:14.543ex; height:5.176ex;" alt="{\displaystyle f_{\rm {D,max}}={\frac {v_{\rm {mob}}}{\lambda _{\rm {c}}}}}"></span> is the maximum Doppler shift due to the mobile station moving (see <a href="/wiki/Rayleigh_fading#Doppler_power_spectral_density" title="Rayleigh fading">Doppler Spread</a>) and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f_{\rm {D,Sat}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">D</mi> <mo>,</mo> <mi mathvariant="normal">S</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">t</mi> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f_{\rm {D,Sat}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cecc4a1102203bfc21197d0f06fc4850d3c36894" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:5.46ex; height:2.843ex;" alt="{\displaystyle f_{\rm {D,Sat}}}"></span> is the additional Doppler shift due to the satellite moving.</figcaption></figure> </td></tr></tbody></table> <div class="mw-heading mw-heading4"><h4 id="Satellite_navigation">Satellite navigation</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Doppler_effect&action=edit&section=12" title="Edit section: Satellite navigation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Satellite_navigation" title="Satellite navigation">Satellite navigation</a></div> <p>The Doppler shift can be exploited for <a href="/wiki/Satellite_navigation" title="Satellite navigation">satellite navigation</a> such as in <a href="/wiki/Transit_(satellite)" title="Transit (satellite)">Transit</a> and <a href="/wiki/DORIS_(satellite_system)" title="DORIS (satellite system)">DORIS</a>. </p> <div class="mw-heading mw-heading4"><h4 id="Satellite_communication">Satellite communication</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Doppler_effect&action=edit&section=13" title="Edit section: Satellite communication"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Satellite_communication" class="mw-redirect" title="Satellite communication">Satellite communication</a></div> <p>Doppler also needs to be compensated in <a href="/wiki/Satellite_communication" class="mw-redirect" title="Satellite communication">satellite communication</a>. Fast moving satellites can have a Doppler shift of dozens of kilohertz relative to a ground station. The speed, thus magnitude of Doppler effect, changes due to earth curvature. Dynamic Doppler compensation, where the frequency of a signal is changed progressively during transmission, is used so the satellite receives a constant frequency signal.<sup id="cite_ref-24" class="reference"><a href="#cite_note-24"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> After realizing that the Doppler shift had not been considered before launch of the <a href="/wiki/Huygens_(spacecraft)#Critical_design_flaw_partially_resolved" title="Huygens (spacecraft)">Huygens probe</a> of the 2005 <a href="/wiki/Cassini%E2%80%93Huygens" title="Cassini–Huygens">Cassini–Huygens</a> mission, the probe trajectory was altered to approach <a href="/wiki/Titan_(moon)" title="Titan (moon)">Titan</a> in such a way that its transmissions traveled perpendicular to its direction of motion relative to Cassini, greatly reducing the Doppler shift.<sup id="cite_ref-TitanCalling_25-0" class="reference"><a href="#cite_note-TitanCalling-25"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> </p><p>Doppler shift of the direct path can be estimated by the following formula:<sup id="cite_ref-26" class="reference"><a href="#cite_note-26"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f_{\rm {D,dir}}={\frac {v_{\rm {mob}}}{\lambda _{\rm {c}}}}\cos \phi \cos \theta }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">D</mi> <mo>,</mo> <mi mathvariant="normal">d</mi> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">r</mi> </mrow> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">o</mi> <mi mathvariant="normal">b</mi> </mrow> </mrow> </msub> <msub> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">c</mi> </mrow> </mrow> </msub> </mfrac> </mrow> <mi>cos</mi> <mo>⁡</mo> <mi>ϕ</mi> <mi>cos</mi> <mo>⁡</mo> <mi>θ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f_{\rm {D,dir}}={\frac {v_{\rm {mob}}}{\lambda _{\rm {c}}}}\cos \phi \cos \theta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4e8f397ac583b0ae4a6236cdb74f23fdb591a5b6" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:23.746ex; height:5.176ex;" alt="{\displaystyle f_{\rm {D,dir}}={\frac {v_{\rm {mob}}}{\lambda _{\rm {c}}}}\cos \phi \cos \theta }"></span> where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v_{\text{mob}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>mob</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v_{\text{mob}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a44578cef60aa8926da7097fdb674b21afa9f995" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.465ex; height:2.009ex;" alt="{\displaystyle v_{\text{mob}}}"></span> is the speed of the mobile station, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \lambda _{\rm {c}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">c</mi> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lambda _{\rm {c}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4dd534f7f2534d6e22f726e0facac0e7aaacd5e8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.318ex; height:2.509ex;" alt="{\displaystyle \lambda _{\rm {c}}}"></span> is the wavelength of the carrier, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \phi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ϕ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \phi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/72b1f30316670aee6270a28334bdf4f5072cdde4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.385ex; height:2.509ex;" alt="{\displaystyle \phi }"></span> is the elevation angle of the satellite and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \theta }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>θ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \theta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6e5ab2664b422d53eb0c7df3b87e1360d75ad9af" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.09ex; height:2.176ex;" alt="{\displaystyle \theta }"></span> is the driving direction with respect to the satellite. </p><p>The additional Doppler shift due to the satellite moving can be described as: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f_{\rm {D,sat}}={\frac {v_{\rm {rel,sat}}}{\lambda _{\rm {c}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">D</mi> <mo>,</mo> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">t</mi> </mrow> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">r</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">l</mi> <mo>,</mo> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">t</mi> </mrow> </mrow> </msub> <msub> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">c</mi> </mrow> </mrow> </msub> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f_{\rm {D,sat}}={\frac {v_{\rm {rel,sat}}}{\lambda _{\rm {c}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/548819ca0fd536255dd362c6d1f5463509a99ffc" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:14.887ex; height:5.509ex;" alt="{\displaystyle f_{\rm {D,sat}}={\frac {v_{\rm {rel,sat}}}{\lambda _{\rm {c}}}}}"></span> where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v_{\rm {rel,sat}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">r</mi> <mi mathvariant="normal">e</mi> <mi mathvariant="normal">l</mi> <mo>,</mo> <mi mathvariant="normal">s</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">t</mi> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v_{\rm {rel,sat}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/22c1700f72e5dad3d5b6059085ea6bdf76341ecc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:5.759ex; height:2.343ex;" alt="{\displaystyle v_{\rm {rel,sat}}}"></span> is the relative speed of the satellite. </p> <div class="mw-heading mw-heading3"><h3 id="Audio">Audio</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Doppler_effect&action=edit&section=14" title="Edit section: Audio"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The <a href="/wiki/Leslie_speaker" title="Leslie speaker">Leslie speaker</a>, most commonly associated with and predominantly used with the famous <a href="/wiki/Hammond_organ" title="Hammond organ">Hammond organ</a>, takes advantage of the Doppler effect by using an electric motor to rotate an acoustic horn around a loudspeaker, sending its sound in a circle. This results at the listener's ear in rapidly fluctuating frequencies of a keyboard note. </p> <div class="mw-heading mw-heading3"><h3 id="Vibration_measurement">Vibration measurement</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Doppler_effect&action=edit&section=15" title="Edit section: Vibration measurement"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A <a href="/wiki/Laser_Doppler_vibrometer" title="Laser Doppler vibrometer">laser Doppler vibrometer</a> (LDV) is a non-contact instrument for measuring vibration. The laser beam from the LDV is directed at the surface of interest, and the vibration amplitude and frequency are extracted from the Doppler shift of the laser beam frequency due to the motion of the surface. </p> <div class="mw-heading mw-heading3"><h3 id="Robotics">Robotics</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Doppler_effect&action=edit&section=16" title="Edit section: Robotics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Dynamic real-time path planning in robotics to aid the movement of robots in a sophisticated environment with moving obstacles often take help of Doppler effect.<sup id="cite_ref-27" class="reference"><a href="#cite_note-27"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup> Such applications are specially used for competitive robotics where the environment is constantly changing, such as robosoccer. </p> <div class="mw-heading mw-heading2"><h2 id="Inverse_Doppler_effect">Inverse Doppler effect</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Doppler_effect&action=edit&section=17" title="Edit section: Inverse Doppler effect"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Since 1968 scientists such as <a href="/wiki/Victor_Veselago" title="Victor Veselago">Victor Veselago</a> have speculated about the possibility of an inverse Doppler effect. The size of the Doppler shift depends on the refractive index of the medium a wave is traveling through. Some materials are capable of <a href="/wiki/Negative_refraction" title="Negative refraction">negative refraction</a>, which should lead to a Doppler shift that works in a direction opposite that of a conventional Doppler shift.<sup id="cite_ref-28" class="reference"><a href="#cite_note-28"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> The first experiment that detected this effect was conducted by Nigel Seddon and Trevor Bearpark in <a href="/wiki/Bristol" title="Bristol">Bristol</a>, <a href="/wiki/United_Kingdom" title="United Kingdom">United Kingdom</a> in 2003.<sup id="cite_ref-29" class="reference"><a href="#cite_note-29"><span class="cite-bracket">[</span>p 5<span class="cite-bracket">]</span></a></sup> Later, the inverse Doppler effect was observed in some inhomogeneous materials, and predicted inside a Vavilov–Cherenkov cone.<sup id="cite_ref-30" class="reference"><a href="#cite_note-30"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Doppler_effect&action=edit&section=18" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1184024115">.mw-parser-output .div-col{margin-top:0.3em;column-width:30em}.mw-parser-output .div-col-small{font-size:90%}.mw-parser-output .div-col-rules{column-rule:1px solid #aaa}.mw-parser-output .div-col dl,.mw-parser-output .div-col ol,.mw-parser-output .div-col ul{margin-top:0}.mw-parser-output .div-col li,.mw-parser-output .div-col dd{page-break-inside:avoid;break-inside:avoid-column}</style><div class="div-col" style="column-width: 30em;"> <ul><li><a href="/wiki/Bistatic_Doppler_shift" class="mw-redirect" title="Bistatic Doppler shift">Bistatic Doppler shift</a></li> <li><a href="/wiki/Differential_Doppler_effect" title="Differential Doppler effect">Differential Doppler effect</a></li> <li><a href="/wiki/Doppler_cooling" title="Doppler cooling">Doppler cooling</a></li> <li><a href="/wiki/Dopplergraph" title="Dopplergraph">Dopplergraph</a></li> <li><a href="/wiki/Fading" title="Fading">Fading</a></li> <li><a href="/wiki/Fizeau_experiment" title="Fizeau experiment">Fizeau experiment</a></li> <li><a href="/wiki/Photoacoustic_Doppler_effect" title="Photoacoustic Doppler effect">Photoacoustic Doppler effect</a></li> <li><a href="/wiki/Range_rate" class="mw-redirect" title="Range rate">Range rate</a></li> <li><a href="/wiki/Rayleigh_fading" title="Rayleigh fading">Rayleigh fading</a></li> <li><a href="/wiki/Redshift" title="Redshift">Redshift</a></li> <li><a href="/wiki/Laser_Doppler_imaging" title="Laser Doppler imaging">Laser Doppler imaging</a></li> <li><a href="/wiki/Relativistic_Doppler_effect" title="Relativistic Doppler effect">Relativistic Doppler effect</a></li></ul> </div> <div class="mw-heading mw-heading2"><h2 id="Primary_sources">Primary sources</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Doppler_effect&action=edit&section=19" title="Edit section: Primary sources"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist reflist-columns references-column-width" style="column-width: 30em;"> <ol class="references"> <li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFBuys_Ballot1845" class="citation journal cs1">Buys Ballot (1845). <a rel="nofollow" class="external text" href="https://zenodo.org/record/1423606">"Akustische Versuche auf der Niederländischen Eisenbahn, nebst gelegentlichen Bemerkungen zur Theorie des Hrn. Prof. Doppler (in German)"</a>. <i>Annalen der Physik und Chemie</i>. <b>142</b> (11): 321–351. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/1845AnP...142..321B">1845AnP...142..321B</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1002%2Fandp.18451421102">10.1002/andp.18451421102</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Annalen+der+Physik+und+Chemie&rft.atitle=Akustische+Versuche+auf+der+Niederl%C3%A4ndischen+Eisenbahn%2C+nebst+gelegentlichen+Bemerkungen+zur+Theorie+des+Hrn.+Prof.+Doppler+%28in+German%29&rft.volume=142&rft.issue=11&rft.pages=321-351&rft.date=1845&rft_id=info%3Adoi%2F10.1002%2Fandp.18451421102&rft_id=info%3Abibcode%2F1845AnP...142..321B&rft.au=Buys+Ballot&rft_id=https%3A%2F%2Fzenodo.org%2Frecord%2F1423606&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADoppler+effect" class="Z3988"></span></span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text">Fizeau: "Acoustique et optique". <i>Lecture, <a href="/wiki/Philomatic_Society" class="mw-redirect" title="Philomatic Society">Société Philomathique</a> de Paris</i>, 29 December 1848. According to Becker(pg. 109), this was never published, but recounted by M. Moigno(1850): "Répertoire d'optique moderne" (in French), vol 3. pp 1165–1203 and later in full by Fizeau, "Des effets du mouvement sur le ton des vibrations sonores et sur la longeur d'onde des rayons de lumière"; [Paris, 1870]. <i>Annales de Chimie et de Physique</i>, 19, 211–221.</span> </li> <li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFScott_Russell1848" class="citation journal cs1">Scott Russell, John (1848). <a rel="nofollow" class="external text" href="http://www.ma.hw.ac.uk/~chris/doppler.html">"On certain effects produced on sound by the rapid motion of the observer"</a>. <i>Report of the Eighteenth Meeting of the British Association for the Advancement of Science</i>. <b>18</b> (7): 37–38<span class="reference-accessdate">. Retrieved <span class="nowrap">2008-07-08</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Report+of+the+Eighteenth+Meeting+of+the+British+Association+for+the+Advancement+of+Science&rft.atitle=On+certain+effects+produced+on+sound+by+the+rapid+motion+of+the+observer&rft.volume=18&rft.issue=7&rft.pages=37-38&rft.date=1848&rft.aulast=Scott+Russell&rft.aufirst=John&rft_id=http%3A%2F%2Fwww.ma.hw.ac.uk%2F~chris%2Fdoppler.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADoppler+effect" class="Z3988"></span></span> </li> <li id="cite_note-21"><span class="mw-cite-backlink"><b><a href="#cite_ref-21">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPetrescu2015" class="citation journal cs1">Petrescu, Florian Ion T (2015). <a rel="nofollow" class="external text" href="https://www.proquest.com/openview/cec7b768b14887621e9494261e122a4c/1?pq-origsite=gscholar&cbl=1226369">"Improving Medical Imaging and Blood Flow Measurement by using a New Doppler Effect Relationship"</a>. <i>American Journal of Engineering and Applied Sciences</i>. <b>8</b> (4): 582–588. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.3844%2Fajeassp.2015.582.588">10.3844/ajeassp.2015.582.588</a></span> – via ProQuest.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=American+Journal+of+Engineering+and+Applied+Sciences&rft.atitle=Improving+Medical+Imaging+and+Blood+Flow+Measurement+by+using+a+New+Doppler+Effect+Relationship&rft.volume=8&rft.issue=4&rft.pages=582-588&rft.date=2015&rft_id=info%3Adoi%2F10.3844%2Fajeassp.2015.582.588&rft.aulast=Petrescu&rft.aufirst=Florian+Ion+T&rft_id=https%3A%2F%2Fwww.proquest.com%2Fopenview%2Fcec7b768b14887621e9494261e122a4c%2F1%3Fpq-origsite%3Dgscholar%26cbl%3D1226369&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADoppler+effect" class="Z3988"></span></span> </li> <li id="cite_note-29"><span class="mw-cite-backlink"><b><a href="#cite_ref-29">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFKozyrevvan_der_Weide2005" class="citation journal cs1">Kozyrev, Alexander B.; van der Weide, Daniel W. (2005). "Explanation of the Inverse Doppler Effect Observed in Nonlinear Transmission Lines". <i>Physical Review Letters</i>. <b>94</b> (20): 203902. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2005PhRvL..94t3902K">2005PhRvL..94t3902K</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1103%2FPhysRevLett.94.203902">10.1103/PhysRevLett.94.203902</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/16090248">16090248</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Physical+Review+Letters&rft.atitle=Explanation+of+the+Inverse+Doppler+Effect+Observed+in+Nonlinear+Transmission+Lines&rft.volume=94&rft.issue=20&rft.pages=203902&rft.date=2005&rft_id=info%3Apmid%2F16090248&rft_id=info%3Adoi%2F10.1103%2FPhysRevLett.94.203902&rft_id=info%3Abibcode%2F2005PhRvL..94t3902K&rft.aulast=Kozyrev&rft.aufirst=Alexander+B.&rft.au=van+der+Weide%2C+Daniel+W.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADoppler+effect" class="Z3988"></span></span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Doppler_effect&action=edit&section=20" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239543626"><div class="reflist"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFUnited_States._Navy_Department1969" class="citation book cs1">United States. Navy Department (1969). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=gjYGC_sc6lcC&pg=PA194"><i>Principles and Applications of Underwater Sound, Originally Issued as Summary Technical Report of Division 6, NDRC, Vol. 7, 1946, Reprinted...1968</i></a>. p. 194<span class="reference-accessdate">. Retrieved <span class="nowrap">2021-03-29</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Principles+and+Applications+of+Underwater+Sound%2C+Originally+Issued+as+Summary+Technical+Report+of+Division+6%2C+NDRC%2C+Vol.+7%2C+1946%2C+Reprinted...1968&rft.pages=194&rft.date=1969&rft.au=United+States.+Navy+Department&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DgjYGC_sc6lcC%26pg%3DPA194&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADoppler+effect" class="Z3988"></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFJoseph2013" class="citation book cs1">Joseph, A. (2013). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=FRVaNZEQCa4C&pg=PA164"><i>Measuring Ocean Currents: Tools, Technologies, and Data</i></a>. Elsevier Science. p. 164. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-12-391428-6" title="Special:BookSources/978-0-12-391428-6"><bdi>978-0-12-391428-6</bdi></a><span class="reference-accessdate">. Retrieved <span class="nowrap">2021-03-30</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Measuring+Ocean+Currents%3A+Tools%2C+Technologies%2C+and+Data&rft.pages=164&rft.pub=Elsevier+Science&rft.date=2013&rft.isbn=978-0-12-391428-6&rft.aulast=Joseph&rft.aufirst=A.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DFRVaNZEQCa4C%26pg%3DPA164&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADoppler+effect" class="Z3988"></span></span> </li> <li id="cite_note-Giordano-3"><span class="mw-cite-backlink">^ <a href="#cite_ref-Giordano_3-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Giordano_3-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGiordano2009" class="citation book cs1">Giordano, Nicholas (2009). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=BwistUlpZ7cC&pg=PA424"><i>College Physics: Reasoning and Relationships</i></a>. Cengage Learning. pp. 421–424. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0534424718" title="Special:BookSources/978-0534424718"><bdi>978-0534424718</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=College+Physics%3A+Reasoning+and+Relationships&rft.pages=421-424&rft.pub=Cengage+Learning&rft.date=2009&rft.isbn=978-0534424718&rft.aulast=Giordano&rft.aufirst=Nicholas&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DBwistUlpZ7cC%26pg%3DPA424&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADoppler+effect" class="Z3988"></span></span> </li> <li id="cite_note-Possel-4"><span class="mw-cite-backlink">^ <a href="#cite_ref-Possel_4-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Possel_4-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPossel2017" class="citation web cs1">Possel, Markus (2017). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20170914003837/http://www.einstein-online.info/spotlights/doppler">"Waves, motion and frequency: the Doppler effect"</a>. <i>Einstein Online, Vol. 5</i>. Max Planck Institute for Gravitational Physics, Potsdam, Germany. Archived from <a rel="nofollow" class="external text" href="http://www.einstein-online.info/spotlights/doppler">the original</a> on September 14, 2017<span class="reference-accessdate">. Retrieved <span class="nowrap">September 4,</span> 2017</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Einstein+Online%2C+Vol.+5&rft.atitle=Waves%2C+motion+and+frequency%3A+the+Doppler+effect&rft.date=2017&rft.aulast=Possel&rft.aufirst=Markus&rft_id=http%3A%2F%2Fwww.einstein-online.info%2Fspotlights%2Fdoppler&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADoppler+effect" class="Z3988"></span></span> </li> <li id="cite_note-Henderson-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-Henderson_5-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHenderson2017" class="citation web cs1">Henderson, Tom (2017). <a rel="nofollow" class="external text" href="http://www.physicsclassroom.com/class/waves/Lesson-3/The-Doppler-Effect">"The Doppler Effect – Lesson 3, Waves"</a>. <i>Physics tutorial</i>. The Physics Classroom<span class="reference-accessdate">. Retrieved <span class="nowrap">September 4,</span> 2017</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Physics+tutorial&rft.atitle=The+Doppler+Effect+%E2%80%93+Lesson+3%2C+Waves&rft.date=2017&rft.aulast=Henderson&rft.aufirst=Tom&rft_id=http%3A%2F%2Fwww.physicsclassroom.com%2Fclass%2Fwaves%2FLesson-3%2FThe-Doppler-Effect&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADoppler+effect" class="Z3988"></span></span> </li> <li id="cite_note-AlecEden-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-AlecEden_6-0">^</a></b></span> <span class="reference-text">Alec Eden <i>The search for Christian Doppler</i>, Springer-Verlag, Wien 1992. 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Becker, <i>Unravelling Starlight: William and Margaret Huggins and the Rise of the New Astronomy</i>, illustrated Edition, <a href="/wiki/Cambridge_University_Press" title="Cambridge University Press">Cambridge University Press</a>, 2011; <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/110700229X" title="Special:BookSources/110700229X">110700229X</a>, 9781107002296.</span> </li> <li id="cite_note-halliday-11"><span class="mw-cite-backlink">^ <a href="#cite_ref-halliday_11-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-halliday_11-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWalkerResnickHalliday2007" class="citation book cs1">Walker, Jearl; <a href="/wiki/Robert_Resnick" title="Robert Resnick">Resnick, Robert</a>; <a href="/wiki/David_Halliday_(physicist)" title="David Halliday (physicist)">Halliday, David</a> (2007). <i>Halliday & Resnick Fundamentals of Physics</i> (8th ed.). 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Macmillan. p. 154.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Theory+of+Sound&rft.pages=154&rft.edition=2&rft.pub=Macmillan&rft.date=1896&rft.aulast=Strutt+%28Lord+Rayleigh%29&rft.aufirst=John+William&rft_id=https%3A%2F%2Farchive.org%2Fstream%2Ftheorysound02raylgoog%23page%2Fn176%2Fmode%2F2up&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADoppler+effect" class="Z3988"></span></span> </li> <li id="cite_note-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-13">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.astro.ucla.edu/~wright/doppler.htm">"Doppler Shift"</a>. <i>astro.ucla.edu</i>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=astro.ucla.edu&rft.atitle=Doppler+Shift&rft_id=http%3A%2F%2Fwww.astro.ucla.edu%2F~wright%2Fdoppler.htm&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADoppler+effect" class="Z3988"></span></span> </li> <li id="cite_note-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-14">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHarrison2000" class="citation book cs1">Harrison, Edward Robert (2000). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=-8PJbcA2lLoC&pg=PA315"><i>Cosmology: The Science of the Universe</i></a> (2nd ed.). Cambridge University Press. pp. 306<i>ff</i>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-521-66148-5" title="Special:BookSources/978-0-521-66148-5"><bdi>978-0-521-66148-5</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Cosmology%3A+The+Science+of+the+Universe&rft.pages=306%27%27ff%27%27&rft.edition=2nd&rft.pub=Cambridge+University+Press&rft.date=2000&rft.isbn=978-0-521-66148-5&rft.aulast=Harrison&rft.aufirst=Edward+Robert&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3D-8PJbcA2lLoC%26pg%3DPA315&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADoppler+effect" class="Z3988"></span></span> </li> <li id="cite_note-Peacock-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-Peacock_15-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFJA_Peacock2008" class="citation arxiv cs1">JA Peacock (2008). "A diatribe on expanding space". <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/0809.4573">0809.4573</a></span> [<a rel="nofollow" class="external text" href="https://arxiv.org/archive/astro-ph">astro-ph</a>].</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=preprint&rft.jtitle=arXiv&rft.atitle=A+diatribe+on+expanding+space&rft.date=2008&rft_id=info%3Aarxiv%2F0809.4573&rft.au=JA+Peacock&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADoppler+effect" class="Z3988"></span></span> </li> <li id="cite_note-Hogg-16"><span class="mw-cite-backlink"><b><a href="#cite_ref-Hogg_16-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBunnHogg2009" class="citation journal cs1">Bunn, E. F.; Hogg, D. W. (2009). "The kinematic origin of the cosmological redshift". <i>American Journal of Physics</i>. <b>77</b> (8): 688–694. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/0808.1081">0808.1081</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2009AmJPh..77..688B">2009AmJPh..77..688B</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1119%2F1.3129103">10.1119/1.3129103</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:1365918">1365918</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=American+Journal+of+Physics&rft.atitle=The+kinematic+origin+of+the+cosmological+redshift&rft.volume=77&rft.issue=8&rft.pages=688-694&rft.date=2009&rft_id=info%3Aarxiv%2F0808.1081&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A1365918%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1119%2F1.3129103&rft_id=info%3Abibcode%2F2009AmJPh..77..688B&rft.aulast=Bunn&rft.aufirst=E.+F.&rft.au=Hogg%2C+D.+W.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADoppler+effect" class="Z3988"></span></span> </li> <li id="cite_note-17"><span class="mw-cite-backlink"><b><a href="#cite_ref-17">^</a></b></span> <span class="reference-text">An excellent review of the topic in technical detail is given here: <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPercivalSamushiaRossShapiro2011" class="citation journal cs1">Percival, Will; Samushia, Lado; Ross, Ashley; Shapiro, Charles; Raccanelli, Alvise (2011). <a rel="nofollow" class="external text" href="https://doi.org/10.1098%2Frsta.2011.0370">"Review article: Redshift-space distortions"</a>. <i>Philosophical Transactions of the Royal Society</i>. <b>369</b> (1957): 5058–67. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2011RSPTA.369.5058P">2011RSPTA.369.5058P</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1098%2Frsta.2011.0370">10.1098/rsta.2011.0370</a></span>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/22084293">22084293</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Philosophical+Transactions+of+the+Royal+Society&rft.atitle=Review+article%3A+Redshift-space+distortions&rft.volume=369&rft.issue=1957&rft.pages=5058-67&rft.date=2011&rft_id=info%3Apmid%2F22084293&rft_id=info%3Adoi%2F10.1098%2Frsta.2011.0370&rft_id=info%3Abibcode%2F2011RSPTA.369.5058P&rft.aulast=Percival&rft.aufirst=Will&rft.au=Samushia%2C+Lado&rft.au=Ross%2C+Ashley&rft.au=Shapiro%2C+Charles&rft.au=Raccanelli%2C+Alvise&rft_id=https%3A%2F%2Fdoi.org%2F10.1098%252Frsta.2011.0370&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADoppler+effect" class="Z3988"></span></span> </li> <li id="cite_note-18"><span class="mw-cite-backlink"><b><a href="#cite_ref-18">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWolff" class="citation web cs1">Wolff, Dipl.-Ing. (FH) Christian. <a rel="nofollow" class="external text" href="http://www.radartutorial.eu/11.coherent/co06.en.html">"Radar Basics"</a>. <i>radartutorial.eu</i><span class="reference-accessdate">. Retrieved <span class="nowrap">14 April</span> 2018</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=radartutorial.eu&rft.atitle=Radar+Basics&rft.aulast=Wolff&rft.aufirst=Dipl.-Ing.+%28FH%29+Christian&rft_id=http%3A%2F%2Fwww.radartutorial.eu%2F11.coherent%2Fco06.en.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADoppler+effect" class="Z3988"></span></span> </li> <li id="cite_note-19"><span class="mw-cite-backlink"><b><a href="#cite_ref-19">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDaviesNewton2017" class="citation journal cs1">Davies, MJ; Newton, JD (2 July 2017). "Non-invasive imaging in cardiology for the generalist". <i>British Journal of Hospital Medicine</i>. <b>78</b> (7): 392–398. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.12968%2Fhmed.2017.78.7.392">10.12968/hmed.2017.78.7.392</a>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/28692375">28692375</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=British+Journal+of+Hospital+Medicine&rft.atitle=Non-invasive+imaging+in+cardiology+for+the+generalist&rft.volume=78&rft.issue=7&rft.pages=392-398&rft.date=2017-07-02&rft_id=info%3Adoi%2F10.12968%2Fhmed.2017.78.7.392&rft_id=info%3Apmid%2F28692375&rft.aulast=Davies&rft.aufirst=MJ&rft.au=Newton%2C+JD&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADoppler+effect" class="Z3988"></span></span> </li> <li id="cite_note-20"><span class="mw-cite-backlink"><b><a href="#cite_ref-20">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAppisTracyFeinstein2015" class="citation journal cs1">Appis, AW; Tracy, MJ; Feinstein, SB (1 June 2015). <a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4676450">"Update on the safety and efficacy of commercial ultrasound contrast agents in cardiac applications"</a>. <i>Echo Research and Practice</i>. <b>2</b> (2): R55–62. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1530%2FERP-15-0018">10.1530/ERP-15-0018</a>. <a href="/wiki/PMC_(identifier)" class="mw-redirect" title="PMC (identifier)">PMC</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4676450">4676450</a></span>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/26693339">26693339</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Echo+Research+and+Practice&rft.atitle=Update+on+the+safety+and+efficacy+of+commercial+ultrasound+contrast+agents+in+cardiac+applications&rft.volume=2&rft.issue=2&rft.pages=R55-62&rft.date=2015-06-01&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC4676450%23id-name%3DPMC&rft_id=info%3Apmid%2F26693339&rft_id=info%3Adoi%2F10.1530%2FERP-15-0018&rft.aulast=Appis&rft.aufirst=AW&rft.au=Tracy%2C+MJ&rft.au=Feinstein%2C+SB&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC4676450&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADoppler+effect" class="Z3988"></span></span> </li> <li id="cite_note-22"><span class="mw-cite-backlink"><b><a href="#cite_ref-22">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFEvansMcDicken2000" class="citation book cs1">Evans, D. H.; McDicken, W. N. (2000). <i>Doppler Ultrasound</i> (2nd ed.). New York: John Wiley and Sons. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-471-97001-9" title="Special:BookSources/978-0-471-97001-9"><bdi>978-0-471-97001-9</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Doppler+Ultrasound&rft.place=New+York&rft.edition=2nd&rft.pub=John+Wiley+and+Sons&rft.date=2000&rft.isbn=978-0-471-97001-9&rft.aulast=Evans&rft.aufirst=D.+H.&rft.au=McDicken%2C+W.+N.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADoppler+effect" class="Z3988"></span><sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citing_sources" title="Wikipedia:Citing sources"><span title="This citation requires a reference to the specific page or range of pages in which the material appears. (June 2015)">page needed</span></a></i>]</sup></span> </li> <li id="cite_note-23"><span class="mw-cite-backlink"><b><a href="#cite_ref-23">^</a></b></span> <span class="reference-text">Otilia Popescuy, Jason S. Harrisz and Dimitrie C. Popescuz, Designing the Communica- tion Sub-System for Nanosatellite CubeSat Missions: Operational and Implementation Perspectives, 2016, IEEE</span> </li> <li id="cite_note-24"><span class="mw-cite-backlink"><b><a href="#cite_ref-24">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFQingchong1999" class="citation book cs1">Qingchong, Liu (1999). "Doppler measurement and compensation in mobile satellite communications systems". <i>MILCOM 1999. IEEE Military Communications. Conference Proceedings (Cat. No.99CH36341)</i>. Vol. 1. pp. 316–320. <a href="/wiki/CiteSeerX_(identifier)" class="mw-redirect" title="CiteSeerX (identifier)">CiteSeerX</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.674.3987">10.1.1.674.3987</a></span>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1109%2Fmilcom.1999.822695">10.1109/milcom.1999.822695</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-7803-5538-5" title="Special:BookSources/978-0-7803-5538-5"><bdi>978-0-7803-5538-5</bdi></a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:12586746">12586746</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Doppler+measurement+and+compensation+in+mobile+satellite+communications+systems&rft.btitle=MILCOM+1999.+IEEE+Military+Communications.+Conference+Proceedings+%28Cat.+No.99CH36341%29&rft.pages=316-320&rft.date=1999&rft_id=https%3A%2F%2Fciteseerx.ist.psu.edu%2Fviewdoc%2Fsummary%3Fdoi%3D10.1.1.674.3987%23id-name%3DCiteSeerX&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A12586746%23id-name%3DS2CID&rft_id=info%3Adoi%2F10.1109%2Fmilcom.1999.822695&rft.isbn=978-0-7803-5538-5&rft.aulast=Qingchong&rft.aufirst=Liu&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADoppler+effect" class="Z3988"></span></span> </li> <li id="cite_note-TitanCalling-25"><span class="mw-cite-backlink"><b><a href="#cite_ref-TitanCalling_25-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFOberg2004" class="citation news cs1">Oberg, James (October 4, 2004). <a rel="nofollow" class="external text" href="https://archive.today/20120914080503/http://spectrum.ieee.org/aerospace/space-flight/titan-calling">"Titan Calling"</a>. <a href="/wiki/IEEE_Spectrum" title="IEEE Spectrum">IEEE Spectrum</a>. 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On Channel Modelling for Land Mobile Satellite Reception (Doctoral dissertation).</span> </li> <li id="cite_note-27"><span class="mw-cite-backlink"><b><a href="#cite_ref-27">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAgarwalGauravNiralaSinha2018" class="citation book cs1">Agarwal, Saurabh; Gaurav, Ashish Kumar; Nirala, Mehul Kumar; Sinha, Sayan (2018). "Potential and Sampling Based RRT Star for Real-Time Dynamic Motion Planning Accounting for Momentum in Cost Function". <i>Neural Information Processing</i>. Lecture Notes in Computer Science. Vol. 11307. pp. 209–221. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2F978-3-030-04239-4_19">10.1007/978-3-030-04239-4_19</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-030-04238-7" title="Special:BookSources/978-3-030-04238-7"><bdi>978-3-030-04238-7</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=Potential+and+Sampling+Based+RRT+Star+for+Real-Time+Dynamic+Motion+Planning+Accounting+for+Momentum+in+Cost+Function&rft.btitle=Neural+Information+Processing&rft.series=Lecture+Notes+in+Computer+Science&rft.pages=209-221&rft.date=2018&rft_id=info%3Adoi%2F10.1007%2F978-3-030-04239-4_19&rft.isbn=978-3-030-04238-7&rft.aulast=Agarwal&rft.aufirst=Saurabh&rft.au=Gaurav%2C+Ashish+Kumar&rft.au=Nirala%2C+Mehul+Kumar&rft.au=Sinha%2C+Sayan&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADoppler+effect" class="Z3988"></span></span> </li> <li id="cite_note-28"><span class="mw-cite-backlink"><b><a href="#cite_ref-28">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://physicsworld.com/a/doppler-shift-is-seen-in-reverse/">"Doppler shift is seen in reverse"</a>. <i>Physics World</i>. 10 March 2011.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Physics+World&rft.atitle=Doppler+shift+is+seen+in+reverse&rft.date=2011-03-10&rft_id=https%3A%2F%2Fphysicsworld.com%2Fa%2Fdoppler-shift-is-seen-in-reverse%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADoppler+effect" class="Z3988"></span></span> </li> <li id="cite_note-30"><span class="mw-cite-backlink"><b><a href="#cite_ref-30">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFShiLinKaminerGao2018" class="citation journal cs1">Shi, Xihang; Lin, Xiao; Kaminer, Ido; Gao, Fei; Yang, Zhaoju; Joannopoulos, John D.; Soljačić, Marin; Zhang, Baile (October 2018). "Superlight inverse Doppler effect". <i>Nature Physics</i>. <b>14</b> (10): 1001–1005. <a href="/wiki/ArXiv_(identifier)" class="mw-redirect" title="ArXiv (identifier)">arXiv</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://arxiv.org/abs/1805.12427">1805.12427</a></span>. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2018arXiv180512427S">2018arXiv180512427S</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1038%2Fs41567-018-0209-6">10.1038/s41567-018-0209-6</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/1745-2473">1745-2473</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:125790662">125790662</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Nature+Physics&rft.atitle=Superlight+inverse+Doppler+effect&rft.volume=14&rft.issue=10&rft.pages=1001-1005&rft.date=2018-10&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A125790662%23id-name%3DS2CID&rft_id=info%3Abibcode%2F2018arXiv180512427S&rft_id=info%3Aarxiv%2F1805.12427&rft.issn=1745-2473&rft_id=info%3Adoi%2F10.1038%2Fs41567-018-0209-6&rft.aulast=Shi&rft.aufirst=Xihang&rft.au=Lin%2C+Xiao&rft.au=Kaminer%2C+Ido&rft.au=Gao%2C+Fei&rft.au=Yang%2C+Zhaoju&rft.au=Joannopoulos%2C+John+D.&rft.au=Solja%C4%8Di%C4%87%2C+Marin&rft.au=Zhang%2C+Baile&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADoppler+effect" class="Z3988"></span></span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Doppler_effect&action=edit&section=21" title="Edit section: Further reading"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li>Doppler, C. (1842). <i><a href="/wiki/%C3%9Cber_das_farbige_Licht_der_Doppelsterne_und_einiger_anderer_Gestirne_des_Himmels" class="mw-redirect" title="Über das farbige Licht der Doppelsterne und einiger anderer Gestirne des Himmels">Über das farbige Licht der Doppelsterne und einiger anderer Gestirne des Himmels (About the coloured light of the binary stars and some other stars of the heavens)</a></i>. Publisher: Abhandlungen der Königl. Böhm. Gesellschaft der Wissenschaften (V. Folge, Bd. 2, S. 465–482) [Proceedings of the Royal Bohemian Society of Sciences (Part V, Vol 2)]; Prague: 1842 (Reissued 1903). Some sources mention 1843 as year of publication because in that year the article was published in the Proceedings of the Bohemian Society of Sciences. Doppler himself referred to the publication as "Prag 1842 bei Borrosch und André", because in 1842 he had a preliminary edition printed that he distributed independently.</li> <li>"Doppler and the Doppler effect", E. N. da C. Andrade, <i>Endeavour</i> Vol. XVIII No. 69, January 1959 (published by ICI London). Historical account of Doppler's original paper and subsequent developments.</li> <li>David Nolte (2020). <i>The fall and rise of the Doppler effect.</i> Physics Today, v. 73, pp. 31–35. <a rel="nofollow" class="external text" href="https://physicstoday.scitation.org/doi/10.1063/PT.3.4429">DOI: 10.1063/PT.3.4429</a></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAdrian1995" class="citation web cs1">Adrian, Eleni (24 June 1995). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20090512192731/http://archive.ncsa.uiuc.edu/Cyberia/Bima/doppler.html">"Doppler Effect"</a>. <a href="/wiki/National_Center_for_Supercomputing_Applications" title="National Center for Supercomputing Applications">NCSA</a>. Archived from <a rel="nofollow" class="external text" href="http://archive.ncsa.uiuc.edu/Cyberia/Bima/doppler.html">the original</a> on 12 May 2009<span class="reference-accessdate">. Retrieved <span class="nowrap">2008-07-13</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Doppler+Effect&rft.pub=NCSA&rft.date=1995-06-24&rft.aulast=Adrian&rft.aufirst=Eleni&rft_id=http%3A%2F%2Farchive.ncsa.uiuc.edu%2FCyberia%2FBima%2Fdoppler.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ADoppler+effect" class="Z3988"></span></li></ul> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Doppler_effect&action=edit&section=22" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Commons-logo.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/12px-Commons-logo.svg.png" decoding="async" 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