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vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">Početak</div> </a> </li> <li id="toc-Formula" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Formula"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Formula</span> </div> </a> <ul id="toc-Formula-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Objašnjenje" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Objašnjenje"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Objašnjenje</span> </div> </a> <ul id="toc-Objašnjenje-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Primene" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Primene"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Primene</span> </div> </a> <button aria-controls="toc-Primene-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Uključi/isključi podsekciju Primene</span> </button> <ul id="toc-Primene-sublist" class="vector-toc-list"> <li id="toc-Svakodnevne_pojave" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Svakodnevne_pojave"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Svakodnevne pojave</span> </div> </a> <ul id="toc-Svakodnevne_pojave-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Astronomija" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Astronomija"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>Astronomija</span> </div> </a> <ul id="toc-Astronomija-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Merenje_temperature" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Merenje_temperature"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.3</span> <span>Merenje temperature</span> </div> </a> <ul id="toc-Merenje_temperature-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">3.4</span> <span>Radar</span> </div> </a> <ul id="toc-Radar-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Crveni_pomak" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Crveni_pomak"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Crveni pomak</span> </div> </a> <ul id="toc-Crveni_pomak-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Izvori" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Izvori"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Izvori</span> </div> </a> <ul id="toc-Izvori-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Povezano" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Povezano"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Povezano</span> </div> </a> <ul id="toc-Povezano-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Vanjske_veze" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Vanjske_veze"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Vanjske veze</span> </div> </a> <ul id="toc-Vanjske_veze-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="Sadržaj" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" lang="sh-Latn" dir="ltr"> <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="Prikaži/sakrij sadržaj" > <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">Prikaži/sakrij sadržaj</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" lang="sh-Latn" dir="ltr"><span class="mw-page-title-main">Dopplerov efekat</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" lang="sh-Latn" dir="ltr"> <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="Prijedi na druge jezične varijante članka. Dostupno je na 85 jezika" > <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 jezika</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 — Afrikanerski" lang="af" hreflang="af" data-title="Doppler-effek" data-language-autonym="Afrikaans" data-language-local-name="Afrikanerski" 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 — Švajcarsko nemački" lang="gsw" hreflang="gsw" data-title="Doppler-Effekt" data-language-autonym="Alemannisch" data-language-local-name="Švajcarsko nemački" 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 — Arapski" lang="ar" hreflang="ar" data-title="تأثير دوبلر" data-language-autonym="العربية" data-language-local-name="Arapski" 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 — Asemijski" lang="as" hreflang="as" data-title="ড'পলাৰ প্ৰভাৱ" data-language-autonym="অসমীয়া" data-language-local-name="Asemijski" 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 — Asturijski" lang="ast" hreflang="ast" data-title="Efeutu Doppler" data-language-autonym="Asturianu" data-language-local-name="Asturijski" 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 — Azerbejdžanski" lang="az" hreflang="az" data-title="Dopler effekti" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbejdžanski" class="interlanguage-link-target"><span>Azərbaycanca</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 — Beloruski" lang="be" hreflang="be" data-title="Эфект Доплера" data-language-autonym="Беларуская" data-language-local-name="Beloruski" 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 — Bugarski" lang="bg" hreflang="bg" data-title="Доплеров ефект" data-language-autonym="Български" data-language-local-name="Bugarski" class="interlanguage-link-target"><span>Български</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 — Bengalski" lang="bn" hreflang="bn" data-title="ডপলার ক্রিয়া" data-language-autonym="বাংলা" data-language-local-name="Bengalski" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-br mw-list-item"><a href="https://br.wikipedia.org/wiki/Efed_Doppler" title="Efed Doppler — Bretonski" lang="br" hreflang="br" data-title="Efed Doppler" data-language-autonym="Brezhoneg" data-language-local-name="Bretonski" class="interlanguage-link-target"><span>Brezhoneg</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Dopplerov_efekt" title="Dopplerov efekt — Bosanski" lang="bs" hreflang="bs" data-title="Dopplerov efekt" data-language-autonym="Bosanski" data-language-local-name="Bosanski" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Efecte_Doppler" title="Efecte Doppler — Katalonski" lang="ca" hreflang="ca" data-title="Efecte Doppler" data-language-autonym="Català" data-language-local-name="Katalonski" class="interlanguage-link-target"><span>Català</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 — centralnokurdski" lang="ckb" hreflang="ckb" data-title="کاریگەریی دۆپلەر" data-language-autonym="کوردی" data-language-local-name="centralnokurdski" class="interlanguage-link-target"><span>کوردی</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 — Češki" lang="cs" hreflang="cs" data-title="Dopplerův jev" data-language-autonym="Čeština" data-language-local-name="Češki" class="interlanguage-link-target"><span>Čeština</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 — Čuvaški" lang="cv" hreflang="cv" data-title="Доплер эффекчĕ" data-language-autonym="Чӑвашла" data-language-local-name="Čuvaški" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Effaith_Doppler" title="Effaith Doppler — Velški" lang="cy" hreflang="cy" data-title="Effaith Doppler" data-language-autonym="Cymraeg" data-language-local-name="Velški" 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 — Danski" lang="da" hreflang="da" data-title="Dopplereffekt" data-language-autonym="Dansk" data-language-local-name="Danski" 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 — Nemački" lang="de" hreflang="de" data-title="Doppler-Effekt" data-language-autonym="Deutsch" data-language-local-name="Nemački" class="interlanguage-link-target"><span>Deutsch</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 — Grčki" lang="el" hreflang="el" data-title="Φαινόμενο Ντόπλερ" data-language-autonym="Ελληνικά" data-language-local-name="Grčki" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Doppler_effect" title="Doppler effect — Engleski" lang="en" hreflang="en" data-title="Doppler effect" data-language-autonym="English" data-language-local-name="Engleski" class="interlanguage-link-target"><span>English</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-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Efecto_Doppler" title="Efecto Doppler — Španski" lang="es" hreflang="es" data-title="Efecto Doppler" data-language-autonym="Español" data-language-local-name="Španski" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Doppleri_efekt" title="Doppleri efekt — Estonski" lang="et" hreflang="et" data-title="Doppleri efekt" data-language-autonym="Eesti" data-language-local-name="Estonski" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Doppler_efektua" title="Doppler efektua — Baskijski" lang="eu" hreflang="eu" data-title="Doppler efektua" data-language-autonym="Euskara" data-language-local-name="Baskijski" 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 — Persijski" lang="fa" hreflang="fa" data-title="اثر دوپلر" data-language-autonym="فارسی" data-language-local-name="Persijski" class="interlanguage-link-target"><span>فارسی</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 — Finski" lang="fi" hreflang="fi" data-title="Doppler-ilmiö" data-language-autonym="Suomi" data-language-local-name="Finski" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Effet_Doppler" title="Effet Doppler — Francuski" lang="fr" hreflang="fr" data-title="Effet Doppler" data-language-autonym="Français" data-language-local-name="Francuski" 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 — Irski" lang="ga" hreflang="ga" data-title="Iarmhairt Doppler" data-language-autonym="Gaeilge" data-language-local-name="Irski" 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 — Galski" lang="gl" hreflang="gl" data-title="Efecto Doppler" data-language-autonym="Galego" data-language-local-name="Galski" class="interlanguage-link-target"><span>Galego</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 — Hebrejski" lang="he" hreflang="he" data-title="אפקט דופלר" data-language-autonym="עברית" data-language-local-name="Hebrejski" class="interlanguage-link-target"><span>עברית</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 — Hrvatski" lang="hr" hreflang="hr" data-title="Dopplerov efekt" data-language-autonym="Hrvatski" data-language-local-name="Hrvatski" class="interlanguage-link-target"><span>Hrvatski</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 — Haićanski" lang="ht" hreflang="ht" data-title="Efè Doppler" data-language-autonym="Kreyòl ayisyen" data-language-local-name="Haićanski" class="interlanguage-link-target"><span>Kreyòl ayisyen</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Doppler-effektus" title="Doppler-effektus — Mađarski" lang="hu" hreflang="hu" data-title="Doppler-effektus" data-language-autonym="Magyar" data-language-local-name="Mađarski" class="interlanguage-link-target"><span>Magyar</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 — Jermenski" lang="hy" hreflang="hy" data-title="Դոպլերի էֆեկտ" data-language-autonym="Հայերեն" data-language-local-name="Jermenski" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Efek_Doppler" title="Efek Doppler — Indonezijski" lang="id" hreflang="id" data-title="Efek Doppler" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonezijski" 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 — Islandski" lang="is" hreflang="is" data-title="Dopplerhrif" data-language-autonym="Íslenska" data-language-local-name="Islandski" 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 — Italijanski" lang="it" hreflang="it" data-title="Effetto Doppler" data-language-autonym="Italiano" data-language-local-name="Italijanski" class="interlanguage-link-target"><span>Italiano</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 — Japanski" lang="ja" hreflang="ja" data-title="ドップラー効果" data-language-autonym="日本語" data-language-local-name="Japanski" class="interlanguage-link-target"><span>日本語</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 — Gruzijski" lang="ka" hreflang="ka" data-title="დოპლერის ეფექტი" data-language-autonym="ქართული" data-language-local-name="Gruzijski" 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 — Kozački" lang="kk" hreflang="kk" data-title="Доплер эффекті" data-language-autonym="Қазақша" data-language-local-name="Kozački" class="interlanguage-link-target"><span>Қазақша</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 — Kanada" lang="kn" hreflang="kn" data-title="ಡಾಪ್ಲರ್ ಪರಿಣಾಮ" data-language-autonym="ಕನ್ನಡ" data-language-local-name="Kanada" class="interlanguage-link-target"><span>ಕನ್ನಡ</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 — Korejski" lang="ko" hreflang="ko" data-title="도플러 효과" data-language-autonym="한국어" data-language-local-name="Korejski" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Effectus_Doppler" title="Effectus Doppler — Latinski" lang="la" hreflang="la" data-title="Effectus Doppler" data-language-autonym="Latina" data-language-local-name="Latinski" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Doplerio_efektas" title="Doplerio efektas — Litvanski" lang="lt" hreflang="lt" data-title="Doplerio efektas" data-language-autonym="Lietuvių" data-language-local-name="Litvanski" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Doplera_efekts" title="Doplera efekts — Letonski" lang="lv" hreflang="lv" data-title="Doplera efekts" data-language-autonym="Latviešu" data-language-local-name="Letonski" class="interlanguage-link-target"><span>Latviešu</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 — Makedonski" lang="mk" hreflang="mk" data-title="Доплеров ефект" data-language-autonym="Македонски" data-language-local-name="Makedonski" 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 — Malajalam" lang="ml" hreflang="ml" data-title="ഡോപ്ലർ പ്രഭാവം" data-language-autonym="മലയാളം" data-language-local-name="Malajalam" 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 — Malajski" lang="ms" hreflang="ms" data-title="Kesan Doppler" data-language-autonym="Bahasa Melayu" data-language-local-name="Malajski" 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 — Burmanski" lang="my" hreflang="my" data-title="ဒေါ့ပလာ အကျိုးသက်ရောက်မှု" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="Burmanski" 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 — Holandski" lang="nl" hreflang="nl" data-title="Dopplereffect" data-language-autonym="Nederlands" data-language-local-name="Holandski" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Dopplereffekten" title="Dopplereffekten — Norveški njorsk" lang="nn" hreflang="nn" data-title="Dopplereffekten" data-language-autonym="Norsk nynorsk" data-language-local-name="Norveški njorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Dopplereffekt" title="Dopplereffekt — Norveški bokmål" lang="nb" hreflang="nb" data-title="Dopplereffekt" data-language-autonym="Norsk bokmål" data-language-local-name="Norveški bokmål" class="interlanguage-link-target"><span>Norsk bokmål</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 — Provansalski" lang="oc" hreflang="oc" data-title="Efècte Doppler" data-language-autonym="Occitan" data-language-local-name="Provansalski" 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 — Orijski" lang="or" hreflang="or" data-title="ଡୋପ୍ଲର୍ ପ୍ରଭାବ" data-language-autonym="ଓଡ଼ିଆ" data-language-local-name="Orijski" class="interlanguage-link-target"><span>ଓଡ଼ିଆ</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 — Pandžabski" lang="pa" hreflang="pa" data-title="ਡਾਪਲਰ ਪ੍ਰਭਾਵ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="Pandžabski" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pl badge-Q17437796 badge-featuredarticle mw-list-item" title="izabrani članci"><a href="https://pl.wikipedia.org/wiki/Efekt_Dopplera" title="Efekt Dopplera — Poljski" lang="pl" hreflang="pl" data-title="Efekt Dopplera" data-language-autonym="Polski" data-language-local-name="Poljski" class="interlanguage-link-target"><span>Polski</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-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-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Efeito_Doppler" title="Efeito Doppler — Portugalski" lang="pt" hreflang="pt" data-title="Efeito Doppler" data-language-autonym="Português" data-language-local-name="Portugalski" 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 — Rumunski" lang="ro" hreflang="ro" data-title="Efectul Doppler" data-language-autonym="Română" data-language-local-name="Rumunski" 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 — Ruski" lang="ru" hreflang="ru" data-title="Эффект Доплера" data-language-autonym="Русский" data-language-local-name="Ruski" class="interlanguage-link-target"><span>Русский</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 — Singaleski" lang="si" hreflang="si" data-title="ඩොප්ලර් ආචරණය" data-language-autonym="සිංහල" data-language-local-name="Singaleski" 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 — Slovački" lang="sk" hreflang="sk" data-title="Dopplerov jav" data-language-autonym="Slovenčina" data-language-local-name="Slovački" 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 — Slovenački" lang="sl" hreflang="sl" data-title="Dopplerjev pojav" data-language-autonym="Slovenščina" data-language-local-name="Slovenački" class="interlanguage-link-target"><span>Slovenščina</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 — Albanski" lang="sq" hreflang="sq" data-title="Efekti i Dopplerit" data-language-autonym="Shqip" data-language-local-name="Albanski" class="interlanguage-link-target"><span>Shqip</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 — Srpski" lang="sr" hreflang="sr" data-title="Доплеров ефекат" data-language-autonym="Српски / srpski" data-language-local-name="Srpski" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Dopplereffekt" title="Dopplereffekt — Švedski" lang="sv" hreflang="sv" data-title="Dopplereffekt" data-language-autonym="Svenska" data-language-local-name="Švedski" class="interlanguage-link-target"><span>Svenska</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 — Svahili" lang="sw" hreflang="sw" data-title="Athari ya Doppler" data-language-autonym="Kiswahili" data-language-local-name="Svahili" class="interlanguage-link-target"><span>Kiswahili</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 — Tamilski" lang="ta" hreflang="ta" data-title="டாப்ளர் விளைவு" data-language-autonym="தமிழ்" data-language-local-name="Tamilski" class="interlanguage-link-target"><span>தமிழ்</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 — Tajlandski" lang="th" hreflang="th" data-title="ปรากฏการณ์ด็อพเพลอร์" data-language-autonym="ไทย" data-language-local-name="Tajlandski" 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srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/7f/Doppler_effect_diagrammatic.svg/375px-Doppler_effect_diagrammatic.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/7f/Doppler_effect_diagrammatic.svg/500px-Doppler_effect_diagrammatic.svg.png 2x" data-file-width="744" data-file-height="238" /></a><figcaption>Promena talasne dužine uzrokovana kretanjem izvora</figcaption></figure> <figure typeof="mw:File/Thumb"><a href="/wiki/Datoteka:Dopplerfrequenz.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/90/Dopplerfrequenz.gif/250px-Dopplerfrequenz.gif" decoding="async" width="250" height="50" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/90/Dopplerfrequenz.gif/375px-Dopplerfrequenz.gif 1.5x, //upload.wikimedia.org/wikipedia/commons/9/90/Dopplerfrequenz.gif 2x" data-file-width="500" data-file-height="100" /></a><figcaption>Animacija prikazuje kako Doplerov efekat utiče na zvuk kola, ili sirene, kad se približavaju, i kad se udaljavaju.</figcaption></figure> <figure typeof="mw:File/Thumb"><a href="/wiki/Datoteka:Doppler_hattyu.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/92/Doppler_hattyu.jpg/250px-Doppler_hattyu.jpg" decoding="async" width="250" height="200" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/92/Doppler_hattyu.jpg/375px-Doppler_hattyu.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/92/Doppler_hattyu.jpg/500px-Doppler_hattyu.jpg 2x" data-file-width="1712" data-file-height="1368" /></a><figcaption>Doplerov efekata protoka vode oko labuda</figcaption></figure> <p><b>Doplerov efekat</b> je promena <a href="/wiki/U%C4%8Destalost" class="mw-redirect" title="Učestalost">učestalosti</a> vala u odnosu na posmatrača, koji se kreće relativno na njegov izvor.<sup id="cite_ref-Giordano_1-0" class="reference"><a href="#cite_note-Giordano-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> Efekat je nazvan po austrijskom fizičaru <a href="/wiki/Christian_Doppler" title="Christian Doppler">Christianu Doppleru</a>, koji ga je opisao <a href="/wiki/1842" title="1842">1842</a>. </p><p>Ako rastojanje između prijemnika i predajnika opada, frekvencija raste, a ako rastojanje između prijemnika i predajnika raste, frekvencija opada. Na primer, Doplerov efekat možemo primetiti u prometu: zvuk vozila dok se približava drugačiji je nego dok se odaljava. </p><p>Doplerov učinak ima primenu u raznim naukama. U <a href="/wiki/Astronomija" title="Astronomija">astronomiji</a> se primjenom Dopplerova učinka mjeri brzina radijalnoga gibanja nebeskih tijela (na primjer male promjene brzine <a href="/wiki/Zvijezda" title="Zvijezda">zvijezda</a> pod utjecajem <a href="/wiki/Planet" class="mw-redirect" title="Planet">planeta</a>, brzine gibanja galaktika). U <a href="/wiki/Promet" class="mw-redirect" title="Promet">prometu</a> se s pomoću Dopplerova učinka i <a href="/wiki/Radar" title="Radar">radara</a> može odrediti brzina kretanja <a href="/wiki/Vozila" class="mw-redirect" title="Vozila">vozila</a>; u <a href="/wiki/Medicina" title="Medicina">medicini</a>, brzina <a href="/wiki/Protok" title="Protok">protoka</a> <a href="/wiki/Krv" title="Krv">krvi</a> (<a href="/w/index.php?title=Ehosonografija&action=edit&redlink=1" class="new" title="Ehosonografija (stranica ne postoji)">ehosonografija</a>).<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> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Formula">Formula</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Dopplerov_efekat&veaction=edit&section=1" title="Uredi odjeljak Formula" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Dopplerov_efekat&action=edit&section=1" title="Uredi kôd odjeljka Formula"><span>uredi kod</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Formula" title="Formula">Formula</a> za izračunavanje frekvencije prijemnika u slučaju relativnog približavanja (tada je u brojiocu "+", a u imeniocu "-") ili relativnog udaljavanja (tada je u brojiocu "-", a u imeniocu "+"): </p> <dl><dd><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 \nu _{L}={\frac {u\pm v_{L}}{u\mp v_{S}}}\cdot \nu _{S}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ν</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>L</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>u</mi> <mo>±</mo> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>L</mi> </mrow> </msub> </mrow> <mrow> <mi>u</mi> <mo>∓</mo> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>S</mi> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>⋅</mo> <msub> <mi>ν</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>S</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nu _{L}={\frac {u\pm v_{L}}{u\mp v_{S}}}\cdot \nu _{S}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/95b36914e4529a6a6d429620ba78e0a5be5c4b53" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:17.204ex; height:5.509ex;" alt="{\displaystyle \nu _{L}={\frac {u\pm v_{L}}{u\mp v_{S}}}\cdot \nu _{S}}"></span></dd></dl> <p>Legenda: </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 \nu _{L}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ν</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>L</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nu _{L}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0af73c510565577898b539d23463e984504f3385" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.5ex; height:2.009ex;" alt="{\displaystyle \nu _{L}}"></span> - frekvencija prijemnika (frekvencija koju slušalac čuje)</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 \nu _{S}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ν</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>S</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nu _{S}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/586139809b0221befe1949465993fee7bb04de4f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.441ex; height:2.009ex;" alt="{\displaystyle \nu _{S}}"></span> - frekvencija predajnika (izvora)</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 u}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>u</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle u}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c3e6bb763d22c20916ed4f0bb6bd49d7470cffd8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:1.676ex;" alt="{\displaystyle u}"></span> - brzina zvuka u vazduhu (330 m/s)</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_{L}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>L</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v_{L}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/95c32ff52ddc40569679c11eaaeb6a6234ad11c4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.479ex; height:2.009ex;" alt="{\displaystyle v_{L}}"></span> - brzina prijemnika (slušaoca)</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_{S}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>S</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v_{S}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5d7e885f65d33c4aa9adb54b8dcb822055ff5b66" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.42ex; height:2.009ex;" alt="{\displaystyle v_{S}}"></span> - brzina predajnika (izvora)</li></ul> <div class="mw-heading mw-heading2"><h2 id="Objašnjenje"><span id="Obja.C5.A1njenje"></span>Objašnjenje</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Dopplerov_efekat&veaction=edit&section=2" title="Uredi odjeljak Objašnjenje" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Dopplerov_efekat&action=edit&section=2" title="Uredi kôd odjeljka Objašnjenje"><span>uredi kod</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Važno je razumeti da se frekvencija zvuka koji izvor emituje u stvari ne menja. Kako bismo razumeli šta se dešava, razmotrimo sledeću analogiju. Neko baca po jednu loptu svake sekunde u pravcu nekog čoveka. Pretpostavimo da se lopte kreću konstantnom brzinom. Ako se osoba koja baca lopte ne pomera (kao ni osoba ka kojoj se lopte bacaju), do čoveka će svakog sekunda stizati po jedna lopta. Međutim, ako se osoba koja baca lopte kreće prema čoveku, do njega će lopte stizati češće. Suprotno važi ako se osoba koja baca lopte kreće od čoveka. </p><p>Ako pokretni izvor emituje talase kroz sredinu, stvarne frekvencije <i><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 \nu }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ν</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nu }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c15bbbb971240cf328aba572178f091684585468" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.232ex; height:1.676ex;" alt="{\displaystyle \nu }"></span></i><sub>0</sub>, tada posmatrač koji miruje u odnosu na sredinu detektuje talase frekvencije <i><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 \nu }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ν</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nu }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c15bbbb971240cf328aba572178f091684585468" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.232ex; height:1.676ex;" alt="{\displaystyle \nu }"></span></i> date formulom: </p> <dl><dd><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 \nu =\nu _{0}\left({\frac {v}{v+v_{s,r}}}\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ν</mi> <mo>=</mo> <msub> <mi>ν</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>v</mi> <mrow> <mi>v</mi> <mo>+</mo> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> <mo>,</mo> <mi>r</mi> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nu =\nu _{0}\left({\frac {v}{v+v_{s,r}}}\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/58c0545ddd788a2d6d053fee0abae2e014af381d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:18.476ex; height:6.176ex;" alt="{\displaystyle \nu =\nu _{0}\left({\frac {v}{v+v_{s,r}}}\right)}"></span></dd></dl> <p>gde je <i>v</i> brzina talasa u sredini, a <i>v</i><sub>s, r</sub> radijalna (duž prave koja spaja izvor i posmatrača) brzina izvora talasa u odnosu na sredinu (pozitivna ako se kreće od posmatrača, a negativna ako se kreće ka posmatraču) prema posmatraču. </p><p>Slična analiza za pokretnog posmatrača i mirujući izvor daje uočenu frekvenciju (brzina posmatrača je predstavljena kao <i>v</i><sub>o</sub>): </p> <dl><dd><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 \nu =\nu _{0}\left(1-{\frac {v_{0}}{v}}\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ν</mi> <mo>=</mo> <msub> <mi>ν</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mrow> <mo>(</mo> <mrow> <mn>1</mn> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mi>v</mi> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nu =\nu _{0}\left(1-{\frac {v_{0}}{v}}\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ae3a7cbc106ae8d9ec67f9815f316368327af601" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:16.717ex; height:4.843ex;" alt="{\displaystyle \nu =\nu _{0}\left(1-{\frac {v_{0}}{v}}\right)}"></span></dd></dl> <p>gde ista konvencija važi: <i>v</i><sub>o</sub> je pozitivno ako se posmatrač udaljava od izvora, a negativno ako se posmatrač približava izvoru. </p><p>Ovo se može uopštiti u jednu vektorsku jednačinu. Uzmimo koordinatni sistem koji miruje u odnosu na sredinu, u kojoj je brzina zvuka <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>. Izvor <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 s}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>s</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle s}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/01d131dfd7673938b947072a13a9744fe997e632" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.09ex; height:1.676ex;" alt="{\displaystyle s}"></span> se kreće brzinom <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}}_{s}}"> <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"> <mi>s</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {v}}_{s}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cf2e35aa3a72fe7aff65a3d0684235219174053e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.179ex; height:2.676ex;" alt="{\displaystyle {\vec {v}}_{s}}"></span> i emituje talase frekvencije <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 \nu _{s}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ν</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nu _{s}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4842619af57678f318297acbdf7c7c201ef8f918" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.152ex; height:2.009ex;" alt="{\displaystyle \nu _{s}}"></span>. Prijemnik <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 r}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0d1ecb613aa2984f0576f70f86650b7c2a132538" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.049ex; height:1.676ex;" alt="{\displaystyle r}"></span> se kreće brzinom <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}}_{r}}"> <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"> <mi>r</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {v}}_{r}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/036d2e1749743bfadf34e4f45d553738a34b1c9d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.149ex; height:2.676ex;" alt="{\displaystyle {\vec {v}}_{r}}"></span>, a jedinični vektor od <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 s}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>s</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle s}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/01d131dfd7673938b947072a13a9744fe997e632" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.09ex; height:1.676ex;" alt="{\displaystyle s}"></span> do <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 r}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0d1ecb613aa2984f0576f70f86650b7c2a132538" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.049ex; height:1.676ex;" alt="{\displaystyle r}"></span> je <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 {n}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>n</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {n}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/49569db585c1b6306d5ffd91161775f67235fae0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:2.343ex;" alt="{\displaystyle {\vec {n}}}"></span> (t.j. <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 {r}}_{r}-{\vec {r}}_{s}={\vec {n}}|{\vec {r}}_{r}-{\vec {r}}_{s}|}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>r</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> </mrow> </msub> <mo>−</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>r</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>n</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>r</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> </mrow> </msub> <mo>−</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>r</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\vec {r}}_{r}-{\vec {r}}_{s}={\vec {n}}|{\vec {r}}_{r}-{\vec {r}}_{s}|}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/502e5b02c4310b7eba15755d75ad7d04b09a20e2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:20.314ex; height:2.843ex;" alt="{\displaystyle {\vec {r}}_{r}-{\vec {r}}_{s}={\vec {n}}|{\vec {r}}_{r}-{\vec {r}}_{s}|}"></span>). Tada se frekvencija <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 \nu _{r}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ν</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nu _{r}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5125eefdfe644f1480e3c6d3935f05b184d651b2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.122ex; height:2.009ex;" alt="{\displaystyle \nu _{r}}"></span> koju prijemnik opaža dobija formulom </p> <dl><dd><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 {\nu _{r}}{\nu _{s}}}={\frac {1-{\vec {n}}\cdot {\vec {v}}_{r}/c}{1-{\vec {n}}\cdot {\vec {v}}_{s}/c}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>ν</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> </mrow> </msub> <msub> <mi>ν</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msub> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>1</mn> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>n</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>⋅</mo> <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"> <mi>r</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>c</mi> </mrow> <mrow> <mn>1</mn> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>n</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>⋅</mo> <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"> <mi>s</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>c</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\nu _{r}}{\nu _{s}}}={\frac {1-{\vec {n}}\cdot {\vec {v}}_{r}/c}{1-{\vec {n}}\cdot {\vec {v}}_{s}/c}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/13207f39d1be2213efea4933f0c28d3533da80d6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:18.347ex; height:6.509ex;" alt="{\displaystyle {\frac {\nu _{r}}{\nu _{s}}}={\frac {1-{\vec {n}}\cdot {\vec {v}}_{r}/c}{1-{\vec {n}}\cdot {\vec {v}}_{s}/c}}}"></span></dd></dl> <p>Ako je <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_{s}\ll c}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msub> <mo>≪</mo> <mi>c</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v_{s}\ll c}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a02108370782b22038a21830a04e0345ffb867fd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.752ex; height:2.176ex;" alt="{\displaystyle v_{s}\ll c}"></span>, tada promena frekvencije zavisi uglavnom od relativne brzine izvora u odnosu na prijemnik: </p> <dl><dd><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 {\nu _{r}}{\nu _{s}}}\approx 1-{\vec {n}}\cdot ({\vec {v}}_{r}-{\vec {v}}_{s})/c}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>ν</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> </mrow> </msub> <msub> <mi>ν</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msub> </mfrac> </mrow> <mo>≈</mo> <mn>1</mn> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>n</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>⋅</mo> <mo stretchy="false">(</mo> <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"> <mi>r</mi> </mrow> </msub> <mo>−</mo> <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"> <mi>s</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>c</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\nu _{r}}{\nu _{s}}}\approx 1-{\vec {n}}\cdot ({\vec {v}}_{r}-{\vec {v}}_{s})/c}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6c6f90a0e9cf4fdc34cbf6e0c9f5714d1befdd88" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:24.31ex; height:5.009ex;" alt="{\displaystyle {\frac {\nu _{r}}{\nu _{s}}}\approx 1-{\vec {n}}\cdot ({\vec {v}}_{r}-{\vec {v}}_{s})/c}"></span></dd></dl> <p>Ili, alternativno: </p> <dl><dd><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 {\Delta \nu }{\nu _{s}}}={\frac {\nu _{r}-\nu _{s}}{\nu _{s}}}\approx -{\vec {n}}\cdot ({\vec {v}}_{r}-{\vec {v}}_{s})/c\,=-{\vec {n}}\cdot ({\Delta }{\vec {v}})/c}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">Δ</mi> <mi>ν</mi> </mrow> <msub> <mi>ν</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msub> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>ν</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>r</mi> </mrow> </msub> <mo>−</mo> <msub> <mi>ν</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msub> </mrow> <msub> <mi>ν</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msub> </mfrac> </mrow> <mo>≈</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>n</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>⋅</mo> <mo stretchy="false">(</mo> <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"> <mi>r</mi> </mrow> </msub> <mo>−</mo> <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"> <mi>s</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>c</mi> <mspace width="thinmathspace" /> <mo>=</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>n</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo>⋅</mo> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Δ</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>v</mi> <mo stretchy="false">→</mo> </mover> </mrow> </mrow> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>c</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\Delta \nu }{\nu _{s}}}={\frac {\nu _{r}-\nu _{s}}{\nu _{s}}}\approx -{\vec {n}}\cdot ({\vec {v}}_{r}-{\vec {v}}_{s})/c\,=-{\vec {n}}\cdot ({\Delta }{\vec {v}})/c}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/76e3c6abec6744da2ecf240e2236d04beff5213e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:49.638ex; height:5.676ex;" alt="{\displaystyle {\frac {\Delta \nu }{\nu _{s}}}={\frac {\nu _{r}-\nu _{s}}{\nu _{s}}}\approx -{\vec {n}}\cdot ({\vec {v}}_{r}-{\vec {v}}_{s})/c\,=-{\vec {n}}\cdot ({\Delta }{\vec {v}})/c}"></span></dd></dl> <p>Svetlosnim talasima nije potrebna sredina za prostiranje, i za tačno razumevanje Doplerovog efekta kod svetlosti je neophodna <a href="/wiki/Posebna_teorija_relativnosti" class="mw-redirect" title="Posebna teorija relativnosti">Specijalna teorija relativnosti</a>. Vidi <a href="/w/index.php?title=Relativisti%C4%8Dki_Doplerov_efekat&action=edit&redlink=1" class="new" title="Relativistički Doplerov efekat (stranica ne postoji)">relativistički Doplerov efekat</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Primene">Primene</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Dopplerov_efekat&veaction=edit&section=3" title="Uredi odjeljak Primene" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Dopplerov_efekat&action=edit&section=3" title="Uredi kôd odjeljka Primene"><span>uredi kod</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Svakodnevne_pojave">Svakodnevne pojave</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Dopplerov_efekat&veaction=edit&section=4" title="Uredi odjeljak Svakodnevne pojave" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Dopplerov_efekat&action=edit&section=4" title="Uredi kôd odjeljka Svakodnevne pojave"><span>uredi kod</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/Datoteka:Doppler-effect-two-police-cars-diagram.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/7f/Doppler-effect-two-police-cars-diagram.png/350px-Doppler-effect-two-police-cars-diagram.png" decoding="async" width="350" height="194" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/7/7f/Doppler-effect-two-police-cars-diagram.png 1.5x" data-file-width="435" data-file-height="241" /></a><figcaption>Stacionarni mikrofon snima promenu tona sirene policijskog automobila dok automobil prolazi pored mikrofona.</figcaption></figure> <p>Ton sirene policijskog automobila koji prolazi pored posmatrača je u početku viši nego kad automobil (i sirena) miruje. Kako automobil prilazi, ton sirene postaje sve dublji, i postaje dublji od tona mirujuće sirene kada automobil prođe pored slušaoca. Astronom <a href="/w/index.php?title=D%C5%BEon_Dobson_(astronom)&action=edit&redlink=1" class="new" title="Džon Dobson (astronom) (stranica ne postoji)">Džon Dobson</a> je ovaj efekat objasnio na sledeći način: </p> <dl><dd><i>Ton sirene se postepeno menja, jer te automobil nije udario.</i></dd></dl> <p>Drugim rečima, da je sirena prilazila posmatraču direktno, ton bi bio konstantan i viši od uobičajenog (jer je <i>v</i><sub>s, r</sub> samo radijalna komponenta brzine) sve dok automobil ne bi udario posmatrača, a zatim bi ton u trenutku skočio na novu, dublju vrednost. Razlika između višeg tona i tona pri mirovanju bi bila ista kao razlika između nižeg tona i tona pri mirovanju. Kako vozilo prolazi <b>pored</b> posmatrača, radijalna brzina nije konstantna, već se menja kao funkcija ugla između njegove linije pogleda i brzine sirene: </p> <dl><dd><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_{s,r}=v_{s}\cdot \cos {\theta }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> <mo>,</mo> <mi>r</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> </mrow> </msub> <mo>⋅</mo> <mi>cos</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>θ</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v_{s,r}=v_{s}\cdot \cos {\theta }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/66e2acf50b5e34ea8b25c90b8b6e344a7cc9873a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:14.827ex; height:2.843ex;" alt="{\displaystyle v_{s,r}=v_{s}\cdot \cos {\theta }}"></span></dd></dl> <p>gde je <i>v</i><sub>s</sub> brzina objekta (izvora talasa) u odnosu na posmatrača, a <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> je ugao između vektora brzine objekta i prave koja vodi od posmatrača ka objektu. </p> <div class="mw-heading mw-heading3"><h3 id="Astronomija">Astronomija</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Dopplerov_efekat&veaction=edit&section=5" title="Uredi odjeljak Astronomija" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Dopplerov_efekat&action=edit&section=5" title="Uredi kôd odjeljka Astronomija"><span>uredi kod</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/Datoteka:Redshift.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6a/Redshift.svg/200px-Redshift.svg.png" decoding="async" width="200" height="355" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6a/Redshift.svg/300px-Redshift.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6a/Redshift.svg/400px-Redshift.svg.png 2x" data-file-width="300" data-file-height="532" /></a><figcaption><a href="/wiki/Crveni_pomeraj" class="mw-redirect" title="Crveni pomeraj">Crveni pomeraj</a> <a href="/wiki/Spektralna_linija" class="mw-redirect" title="Spektralna linija">spektralnih linija</a> u optičkom spektru superklastera udaljenih galaksija (desno), u poređenju sa Suncem (levo).</figcaption></figure> <p>Doplerov efekat kod <a href="/wiki/Elektromagnetni_talasi" class="mw-redirect" title="Elektromagnetni talasi">elektromagnetnih talasa</a> kao što je svetlost, je od velikog značaja u <a href="/wiki/Astronomija" title="Astronomija">astronomiji</a>, i dovodi do takozvanog <a href="/wiki/Crveni_pomeraj" class="mw-redirect" title="Crveni pomeraj">crvenog pomeraja</a> ili <a href="/w/index.php?title=Plavi_pomeraj&action=edit&redlink=1" class="new" title="Plavi pomeraj (stranica ne postoji)">plavog pomeraja</a>. Koristi se za merenje brzine kojom nam se <a href="/wiki/Zvijezda" title="Zvijezda">zvezde</a> ili <a href="/wiki/Galaksija" title="Galaksija">galaksije</a> primiču ili odmiču. </p><p>Doplerov efekat za svetlost je od koristi u astronomiji zahvaljujući činjenici da spektar kojim zvezde zrače nije neprekidan. Zvezde pokazuju <a href="/wiki/Spektralna_linija" class="mw-redirect" title="Spektralna linija">apsorpcione linije</a> na frekvencijama koje su u vezi sa energijama neophodnim da pobude <a href="/wiki/Elektron" title="Elektron">elektrone</a> različitih hemijskih elemenata da pređu sa jednog energetskog nivoa na drugi. Doplerov efekat je prepoznatljiv u činjenici da apsorpcione linije nisu uvek na frekvencijama koje se dobijaju kod statičnog izvora svetla. Kako plavo svetlo ima veću frekvenciju nego crveno svetlo, spektralne linije svetla koje emituju prilazeća astronomska tela se pomeraju ka plavoj, dok se spektralne linije kod tela koja se odmiču pomeraju ka crvenoj boji. </p><p>Takođe, Doplerov efekat (<a href="/wiki/Crveni_pomeraj" class="mw-redirect" title="Crveni pomeraj">crveni pomeraj</a>) svetlosti udaljenih galaksija poslužio je i kao osnova za formulisanje <a href="/wiki/Hablov_zakon" title="Hablov zakon">Hablovog zakona</a>, koji danas služi za grubu procenu udaljenih <a href="/wiki/Svemir" title="Svemir">svemirskih</a> objekata. </p> <div class="mw-heading mw-heading3"><h3 id="Merenje_temperature">Merenje temperature</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Dopplerov_efekat&veaction=edit&section=6" title="Uredi odjeljak Merenje temperature" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Dopplerov_efekat&action=edit&section=6" title="Uredi kôd odjeljka Merenje temperature"><span>uredi kod</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Još jedna primena Doplerovog efekta, koja se najčešće sreće u astronomiji, je procena temperature gasa koji emituje spektralnu liniju. Usled termalnog kretanja gasa, svaki emiter može biti pomeren malo ka plavoj ili crvenoj, a ukupan efekat ovoga je širenje linije. Ovako dobijen oblik linije se naziva Doplerovim profilom, i širina linije je proporcionalna kvadratnom korenu temperature gasa. Zahvaljujući ovome možemo da koristimo ove linije za merenje temperature emitujućeg gasa. </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=Dopplerov_efekat&veaction=edit&section=7" title="Uredi odjeljak Radar" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Dopplerov_efekat&action=edit&section=7" title="Uredi kôd odjeljka Radar"><span>uredi kod</span></a><span class="mw-editsection-bracket">]</span></span></div> <dl><dd><div class="noprint relarticle mainarticle"><i>Glavni članak: <a href="/w/index.php?title=Dopler_radar&action=edit&redlink=1" class="new" title="Dopler radar (stranica ne postoji)">Dopler radar</a></i></div></dd></dl> <p>Doplerov efekat se koristi i u nekim vrstama <a href="/wiki/Radar" title="Radar">radara</a>, kako bi se izmerila brzina detektovanog objekta. Zrak iz radara se ispaljuje prema pokretnoj meti (na primer automobilu, jer ovakve radare često koristi policija za otkrivanje prebrze vožnje), dok se meta udaljava od radara. Svaki naredni talas mora da pređe veću razdaljinu kako bi pogodio metu, pre nego što se odbije nazad ka izvoru. Kako svaki sledeći talas putuje duže, razmak između njih se povećava, pa se povećava i <a href="/wiki/Talasna_du%C5%BEina" class="mw-redirect" title="Talasna dužina">talasna dužina</a> (a frekvencija se smanjuje). Radarski zrak može da se ispaljuje i prema meti koja se približava, i u tom slučaju svaki naredni talas prelazi manju razdaljinu, pa se talasna dužina smanjuje (a frekvencija povećava). </p> <div class="mw-heading mw-heading2"><h2 id="Crveni_pomak">Crveni pomak</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Dopplerov_efekat&veaction=edit&section=8" title="Uredi odjeljak Crveni pomak" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Dopplerov_efekat&action=edit&section=8" title="Uredi kôd odjeljka Crveni pomak"><span>uredi kod</span></a><span class="mw-editsection-bracket">]</span></span></div> <dl><dd><div class="noprint relarticle mainarticle"><i>Glavni članak: <a href="/wiki/Crveni_pomak" title="Crveni pomak">Crveni pomak</a></i></div></dd></dl> <p><b>Crveni pomak</b> je pomak <a href="/wiki/Spektar_(fizika)" class="mw-redirect" title="Spektar (fizika)">spektralnih linija</a> <a href="/wiki/Svjetlost" class="mw-redirect" title="Svjetlost">svjetlosti</a> (povećanje <a href="/wiki/Valna_duljina" class="mw-redirect" title="Valna duljina">valnih duljina</a>) prema <a href="/wiki/Infracrveno_zra%C4%8Denje" title="Infracrveno zračenje">crvenom dijelu spektra</a>. Općenitije, pomak spektralnih linija <a href="/wiki/Elektromagnetsko_zra%C4%8Denje" title="Elektromagnetsko zračenje">elektromagnetskih valova</a> prema većim valnim duljinama u spektru. Nastaje kad se izvor elektromagnetskih valova udaljava, što je brže udaljavanje izvor veći je crveni pomak (Dopplerov učinak) ili kad se izvor elektromagnetskih valova nalazi u snažnom <a href="/wiki/Gravitacijsko_polje" class="mw-redirect" title="Gravitacijsko polje">gravitacijskom polju</a>, a emitirani se valovi šire prema slabijem gravitacijskom polju. Kozmički crveni pomak odražava opće širenje <a href="/wiki/Svemir" title="Svemir">svemira</a> (<a href="/wiki/Hubbleov_zakon" class="mw-redirect" title="Hubbleov zakon">Hubbleov zakon</a>). Gravitacijski crveni pomak nastaje gubitkom energije <a href="/wiki/Foton" title="Foton">fotona</a> u gravitacijskome polju. Dokazan je <a href="/wiki/M%C3%B6ssbauerov_efekt" class="mw-redirect" title="Mössbauerov efekt">Mössbauerovim učinkom</a> i zapažen je u spektrima <a href="/wiki/Zvijezda" title="Zvijezda">zvijezda</a> s jakim gravitacijskim poljem.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Izvori">Izvori</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Dopplerov_efekat&veaction=edit&section=9" title="Uredi odjeljak Izvori" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Dopplerov_efekat&action=edit&section=9" title="Uredi kôd odjeljka Izvori"><span>uredi kod</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r41378145">.mw-parser-output .reflist{font-size:90%;margin-bottom:0.5em;list-style-type:decimal}.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 reflist-columns-2"> <ol class="references"> <li id="cite_note-Giordano-1"><span class="mw-cite-backlink"><a href="#cite_ref-Giordano_1-0">↑</a></span> <span class="reference-text"><span class="citation book">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. str. 421–424. <a href="/wiki/International_Standard_Book_Number" class="mw-redirect" title="International Standard Book Number">ISBN</a> <a href="/wiki/Posebno:Tra%C5%BEi_ISBN/978-0534424718" title="Posebno:Traži ISBN/978-0534424718">978-0534424718</a>.</span><span class="Z3988" 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.aulast=Giordano&rft.aufirst=Nicholas&rft.au=Giordano%2C%26%2332%3BNicholas&rft.date=2009&rft.pages=str.%26nbsp%3B421%E2%80%93424&rft.pub=Cengage+Learning&rft.isbn=978-0534424718&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DBwistUlpZ7cC%26pg%3DPA424&rfr_id=info:sid/en.wikipedia.org:Dopplerov_efekat"><span style="display: none;"> </span></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><a href="#cite_ref-2">↑</a></span> <span class="reference-text"><b>Dopplerov efekt</b>, <a rel="nofollow" class="external autonumber" href="http://www.enciklopedija.hr/natuknica.aspx?id=15974">[1]</a> "Hrvatska enciklopedija", Leksikografski zavod Miroslav Krleža, www.enciklopedija.hr, 2016.</span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><a href="#cite_ref-3">↑</a></span> <span class="reference-text"><b>crveni pomak</b>, <a rel="nofollow" class="external autonumber" href="http://www.enciklopedija.hr/Natuknica.aspx?ID=68995">[2]</a> "Hrvatska enciklopedija", Leksikografski zavod Miroslav Krleža, www.enciklopedija.hr, 2016.</span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="Povezano">Povezano</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Dopplerov_efekat&veaction=edit&section=10" title="Uredi odjeljak Povezano" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Dopplerov_efekat&action=edit&section=10" title="Uredi kôd odjeljka Povezano"><span>uredi kod</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Crveni_pomak" title="Crveni pomak">Crveni pomak</a></li> <li><a href="/w/index.php?title=Plavi_pomak&action=edit&redlink=1" class="new" title="Plavi pomak (stranica ne postoji)">Plavi pomak</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Vanjske_veze">Vanjske veze</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Dopplerov_efekat&veaction=edit&section=11" title="Uredi odjeljak Vanjske veze" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Dopplerov_efekat&action=edit&section=11" title="Uredi kôd odjeljka Vanjske veze"><span>uredi kod</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="infobox sisterproject" style="width: 300px"> <div style="float: left;"><figure class="mw-halign-none" typeof="mw:File"><a href="https://commons.wikimedia.org/wiki/Category:Doppler_effect" title="commons:Category:Doppler effect"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/15px-Commons-logo.svg.png" decoding="async" width="15" height="20" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/23px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/30px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></a><figcaption></figcaption></figure></div> <div style="margin-left: 20px;"><i><b><a href="https://commons.wikimedia.org/wiki/Category:Doppler_effect" class="extiw" title="commons:Category:Doppler effect">Dopplerov efekat</a></b></i> na <a href="https://commons.wikimedia.org/wiki/Glavna_stranica_-_%D0%93%D0%BB%D0%B0%D0%B2%D0%BD%D0%B0_%D1%81%D1%82%D1%80%D0%B0%D0%BD%D0%B8%D1%86%D0%B0" class="extiw" title="commons:Glavna stranica - Главна страница">Wikimedijinoj ostavi</a> </div> </div> <ul><li><a rel="nofollow" class="external text" href="http://scienceworld.wolfram.com/physics/DopplerEffect.html">Doppler Effect</a>, [ScienceWorld]</li> <li><a rel="nofollow" class="external text" href="http://www.falstad.com/ripple/ex-doppler.html">Java simulation of Doppler effect</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20051129174216/http://www.falstad.com/ripple/ex-doppler.html">Arhivirano</a> 2005-11-29 na <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine-u</a></li> <li><a rel="nofollow" class="external text" href="http://www.mathpages.com/rr/s2-04/2-04.htm">Doppler Shift for Sound and Light</a> at MathPages</li> <li><a rel="nofollow" class="external text" href="http://scratch.mit.edu/projects/12532039/">Flash simulation and game of Doppler effect of sound</a> at Scratch (programming language)</li></ul> <div class="navbox-styles nomobile"><style 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style="width:100%;padding:0"><div style="padding:0 0.25em"> <span style="white-space:nowrap"> <a href="/wiki/Svetlost" title="Svetlost">Svetlost</a> <b>•</b></span> <span style="white-space:nowrap"> <a href="/wiki/Val" title="Val">Val</a> <b>•</b></span> <span style="white-space:nowrap"> <a href="/wiki/Osnovne_sile" title="Osnovne sile">Osnovne sile</a> <b>•</b></span> <span style="white-space:nowrap"> <a href="/wiki/Energija" title="Energija">Energija</a> <b>•</b></span> <span style="white-space:nowrap"> <a href="/wiki/Materija" title="Materija">Materija</a> <b>•</b></span> <span style="white-space:nowrap"> <a href="/wiki/Masa" title="Masa">Masa</a> <b>•</b></span> <span style="white-space:nowrap"> <a href="/wiki/Etar_(fizika)" title="Etar (fizika)">Etar</a> <b>•</b></span> <span style="white-space:nowrap"> <a href="/wiki/Kretanje" title="Kretanje">Kretanje</a> <b>•</b></span> <span style="white-space:nowrap"> <a href="/wiki/Gravitacija" title="Gravitacija">Gravitacija</a> <b>•</b></span> <span style="white-space:nowrap"> <a href="/wiki/Elektricitet" title="Elektricitet">Elektricitet</a> <b>•</b></span> <span style="white-space:nowrap"> <a href="/wiki/Sila" title="Sila">Sila</a> <b>•</b></span> <span style="white-space:nowrap"> <a href="/wiki/Tromost" class="mw-redirect" title="Tromost">Tromost</a> <b>•</b></span> <span style="white-space:nowrap"> <a href="/wiki/Valno-%C4%8Desti%C4%8Dni_dualizam" title="Valno-čestični dualizam">Valno-čestični dualizam</a> <b>•</b></span> <span style="white-space:nowrap"> <a href="/wiki/Prostorvreme" title="Prostorvreme">Prostorvreme</a> <b>•</b></span> <span style="white-space:nowrap"> <a href="/wiki/Entropija" title="Entropija">Entropija</a></span></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Kategorija:Podru%C4%8Dja_fizike" title="Kategorija:Područja fizike">Područja</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <span style="white-space:nowrap"> <a href="/wiki/Astronomija" title="Astronomija">Astronomija</a> <b>•</b></span> <span style="white-space:nowrap"> <a href="/wiki/Kosmologija" title="Kosmologija">Kosmologija</a> <b>•</b></span> <span style="white-space:nowrap"> <a href="/wiki/Optika" title="Optika">Optika</a> <b>•</b></span> <span style="white-space:nowrap"> <a href="/wiki/Mehanika" title="Mehanika">Mehanika</a> <b>•</b></span> <span style="white-space:nowrap"> <a href="/wiki/Elektrostatika" title="Elektrostatika">Elektrostatika</a>  <b>•</b></span> <span style="white-space:nowrap"> <a href="/wiki/Elektromagnetizam" title="Elektromagnetizam">Elektromagnetizam</a> <b>•</b></span> <span style="white-space:nowrap"> <a href="/wiki/Termodinamika" title="Termodinamika">Termodinamika</a> <b>•</b></span> <span style="white-space:nowrap"> <a href="/wiki/Kvantna_fizika" class="mw-redirect" title="Kvantna fizika">Kvantna fizika</a> </span></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Kategorija:Pokusi_iz_fizike" title="Kategorija:Pokusi iz fizike">Pokusi</a> i <br /> <a href="/w/index.php?title=Kategorija:Otkri%C4%87a_u_fizici&action=edit&redlink=1" class="new" title="Kategorija:Otkrića u fizici (stranica ne postoji)">otkrića</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%;padding-left:0em;padding-right:0em;"><div style="padding:0em 0.75em;">Antička</div></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"><a href="/wiki/Atom" title="Atom">Teorija atoma</a> <b>•</b> <span style="white-space:nowrap"> <a href="/wiki/O_veli%C4%8Dini_i_udaljenosti_Sunca_i_Mjeseca" title="O veličini i udaljenosti Sunca i Mjeseca">Udaljenost Sunca i Meseca</a> <b>•</b></span> <span style="white-space:nowrap"> <a href="/wiki/Arhimedov_zakon" title="Arhimedov zakon">Arhimedov zakon</a> <b>•</b></span> <span style="white-space:nowrap"> <a href="/wiki/Eratosten#Određivanje_obima_Zemlje" title="Eratosten">Obim zemlje</a> <b>•</b></span> <span style="white-space:nowrap"> <a href="/w/index.php?title=Teorija_impetusa&action=edit&redlink=1" class="new" title="Teorija impetusa (stranica ne postoji)">Teorija impetusa</a> <b>•</b></span> <span style="white-space:nowrap"> <a href="/wiki/Knjiga_o_optici" title="Knjiga o optici">Alhazenova optika</a></span></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;padding-left:0em;padding-right:0em;"><div style="padding:0em 0.75em;"><a href="/wiki/Klasi%C4%8Dna_fizika" title="Klasična fizika">Klasična</a></div></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"><a href="/wiki/Heliocentrizam" title="Heliocentrizam">Kopernikov sustav</a> <b>•</b> <span style="white-space:nowrap"> <a href="/wiki/Snellov_zakon" title="Snellov zakon">Snellov zakon</a> <b>•</b></span> <span style="white-space:nowrap"> <a href="/wiki/Keplerovi_zakoni_planetarnog_kretanja" title="Keplerovi zakoni planetarnog kretanja">Keplerovi zakoni planetarnog kretanja</a> <b>•</b></span> <span style="white-space:nowrap"> <a href="/wiki/Slobodni_pad" title="Slobodni pad">Slobodni pad</a> <b>•</b></span> <span style="white-space:nowrap"> <a href="/wiki/Kretanje_hica" title="Kretanje hica">Kretanje hica</a> <b>•</b></span> <span style="white-space:nowrap"> <a href="/wiki/Galileijeva_relativnost" title="Galileijeva relativnost">Galileijeva relativnost</a> <b>•</b></span> <span style="white-space:nowrap"> <a href="/wiki/Pascalov_zakon" title="Pascalov zakon">Pascalov zakon</a> <b>•</b></span> <span style="white-space:nowrap"> <a href="/wiki/Hookeov_zakon" title="Hookeov zakon">Hookeov zakon</a> <b>•</b></span> <span style="white-space:nowrap"> <a href="/wiki/Boyle-Mariotteov_zakon" title="Boyle-Mariotteov zakon">Boyleov zakon</a> <b>•</b></span> <span style="white-space:nowrap"> <a href="/wiki/Brzina_svjetlosti" title="Brzina svjetlosti">Brzina svjetlosti</a> <b>•</b></span> <span style="white-space:nowrap"> <a href="/w/index.php?title=Opticks&action=edit&redlink=1" class="new" title="Opticks (stranica ne postoji)">Njutnova teorija boja</a> <b>•</b></span> <span style="white-space:nowrap"> <a href="/wiki/Newtonovi_zakoni_kretanja" title="Newtonovi zakoni kretanja">Newtonovi zakoni kretanja</a> <b>•</b></span> <span style="white-space:nowrap"> <a href="/wiki/Newtonov_zakon_gravitacije" title="Newtonov zakon gravitacije">Newtonov zakon gravitacije</a> <b>•</b></span> <span style="white-space:nowrap"> <a href="/wiki/Huygensov_princip" title="Huygensov princip">Huygensov princip</a> <b>•</b></span> <span style="white-space:nowrap"> <a href="/wiki/Zakon_odr%C5%BEanja_mase" title="Zakon održanja mase">Zakon održanja mase</a> <b>•</b></span> <span style="white-space:nowrap"> <a href="/wiki/Coulombov_zakon" title="Coulombov zakon">Kulonov zakon</a> <b>•</b></span> <span style="white-space:nowrap"> <a href="/wiki/Svetlost#Valna_teorija" title="Svetlost">Valna teorija svetla</a> <b>•</b></span> <span style="white-space:nowrap"> <a href="/wiki/Atomska_teorija" title="Atomska teorija">Atomska teorija</a> <b>•</b></span> <span style="white-space:nowrap"> <a href="/wiki/Amp%C3%A8reov_zakon_kru%C5%BEenja" class="mw-redirect" title="Ampèreov zakon kruženja">Ampèreov zakon</a> <b>•</b></span> <span style="white-space:nowrap"> <a href="/wiki/Ohmov_zakon" title="Ohmov zakon">Ohmov zakon</a> <b>•</b></span> <span style="white-space:nowrap"> <a href="/wiki/Faradayev_zakon_indukcije" title="Faradayev zakon indukcije">Faradayev zakon indukcije</a> <b>•</b></span> <span style="white-space:nowrap"> <a href="/wiki/Gaussov_zakon_elektri%C4%8Dnoga_polja" title="Gaussov zakon električnoga polja">Gaussov zakon</a> <b>•</b></span> <span style="white-space:nowrap"> <a href="/wiki/Zakon_o%C4%8Duvanja_energije" title="Zakon očuvanja energije">Zakon očuvanja energije</a> <b>•</b></span> <span style="white-space:nowrap"> <a class="mw-selflink selflink">Dopplerov efekat</a> <b>•</b></span> <span style="white-space:nowrap"> <a href="/wiki/Drugi_zakon_termodinamike" title="Drugi zakon termodinamike">Drugi zakon termodinamike</a> <b>•</b></span> <span style="white-space:nowrap"> <a href="/wiki/Foucaultovo_klatno" title="Foucaultovo klatno">Foucaultovo klatno</a> <b>•</b></span> <span style="white-space:nowrap"> <a href="/wiki/Maxwellove_jednad%C5%BEbe" title="Maxwellove jednadžbe">Maxwellove jednadžbe</a> <b>•</b></span> <span style="white-space:nowrap"> <a href="/wiki/Michelson%E2%80%93Morleyjev_eksperiment" title="Michelson–Morleyjev eksperiment">Michelson–Morleyjev eksperiment</a> <b>•</b></span> <span style="white-space:nowrap"> <a href="/wiki/Elektromagnetsko_zra%C4%8Denje" title="Elektromagnetsko zračenje">Elektromagnetsko zračenje</a></span></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;padding-left:0em;padding-right:0em;"><div style="padding:0em 0.75em;"><a href="/wiki/Kvantna_mehanika" title="Kvantna mehanika">Moderna</a></div></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0;width:auto;"><div style="padding:0 0.25em"><a href="/wiki/Lorentzove_transformacije" title="Lorentzove transformacije">Lorentzove transformacije</a> <b>•</b> <span style="white-space:nowrap"> <a href="/wiki/Kvant" title="Kvant">Kvant</a> <b>•</b></span> <span style="white-space:nowrap"> <a href="/wiki/Fotoelektri%C4%8Dni_efekt" title="Fotoelektrični efekt">Fotoelektrični efekt</a> <b>•</b></span> <span style="white-space:nowrap"> <a href="/wiki/Brownovo_kretanje" title="Brownovo kretanje">Brownovo kretanje</a> <b>•</b></span> <span style="white-space:nowrap"> <a href="/wiki/X-zrake" title="X-zrake">X-zrake</a> <b>•</b></span> <span style="white-space:nowrap"> <a href="/wiki/Elektron" title="Elektron">Elektron</a> <b>•</b></span> <span style="white-space:nowrap"> <a href="/wiki/Specijalna_teorija_relativnosti" title="Specijalna teorija relativnosti">Specijalna relativnost</a> (<a href="/wiki/Ekvivalentnost_mase_i_energije" title="Ekvivalentnost mase i energije">ekvivalentnost mase i energije</a>) <b>•</b></span> <span style="white-space:nowrap"> <a href="/wiki/Foton" title="Foton">Foton</a> <b>•</b></span> <span style="white-space:nowrap"> <a href="/wiki/Atomsko_jezgro" title="Atomsko jezgro">Atomsko jezgro</a> <b>•</b></span> <span style="white-space:nowrap"> <a href="/wiki/Bohrov_model_atoma" title="Bohrov model atoma">Bohrov model atoma</a> <b>•</b></span> <span style="white-space:nowrap"> <a href="/wiki/Op%C5%A1ta_teorija_relativnosti" title="Opšta teorija relativnosti">Opšta relativnost</a> <b>•</b></span> <span style="white-space:nowrap"> <a href="/wiki/Valovi_tvari" title="Valovi tvari">Valovi tvari</a> <b>•</b></span> <span style="white-space:nowrap"> <a href="/wiki/%C5%A0irenje_svemira" title="Širenje svemira">Širenje svemira</a> <b>•</b></span> <span style="white-space:nowrap"> <a href="/wiki/%C5%A0redingerova_jedna%C4%8Dina" class="mw-redirect" title="Šredingerova jednačina">Šredingerova jednačina</a> <b>•</b></span> <span style="white-space:nowrap"> <a href="/wiki/Na%C4%8Delo_neodre%C4%91enosti" title="Načelo neodređenosti">Načelo neodređenosti</a> <b>•</b></span> <span style="white-space:nowrap"> <a href="/wiki/Neutron" title="Neutron">Neutron</a> <b>•</b></span> <span style="white-space:nowrap"> <a href="/wiki/Nuklearna_fisija" title="Nuklearna fisija">Nuklearna fisija</a> i <a href="/wiki/Nuklearna_fuzija" title="Nuklearna fuzija">fuzija</a> <b>•</b></span> <span style="white-space:nowrap"> <a href="/wiki/Pulsar" 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