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class="vector-toc-numb">2</span> <span>Electromagnetics</span> </div> </a> <button aria-controls="toc-Electromagnetics-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>Toggle Electromagnetics subsection</span> </button> <ul id="toc-Electromagnetics-sublist" class="vector-toc-list"> <li id="toc-Resonant_circuits" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Resonant_circuits"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Resonant circuits</span> </div> </a> <ul id="toc-Resonant_circuits-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Cavity_resonators" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Cavity_resonators"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>Cavity resonators</span> </div> </a> <ul id="toc-Cavity_resonators-sublist" class="vector-toc-list"> <li id="toc-Cavity_magnetron" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Cavity_magnetron"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2.1</span> <span>Cavity magnetron</span> </div> </a> <ul id="toc-Cavity_magnetron-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Klystron" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Klystron"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2.2</span> <span>Klystron</span> </div> </a> <ul id="toc-Klystron-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Application_in_particle_accelerators" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Application_in_particle_accelerators"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2.3</span> <span>Application in particle accelerators</span> </div> </a> <ul id="toc-Application_in_particle_accelerators-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Loop-gap_resonator" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Loop-gap_resonator"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3</span> <span>Loop-gap resonator</span> </div> </a> <ul id="toc-Loop-gap_resonator-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Dielectric_resonators" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Dielectric_resonators"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.4</span> <span>Dielectric resonators</span> </div> </a> <ul id="toc-Dielectric_resonators-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Transmission-line_resonators" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Transmission-line_resonators"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.5</span> <span>Transmission-line resonators</span> </div> </a> <ul id="toc-Transmission-line_resonators-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Optical_cavities" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Optical_cavities"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.6</span> <span>Optical cavities</span> </div> </a> <ul id="toc-Optical_cavities-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Mechanical" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Mechanical"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Mechanical</span> </div> </a> <ul id="toc-Mechanical-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Acoustic" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Acoustic"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Acoustic</span> </div> </a> <button aria-controls="toc-Acoustic-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>Toggle Acoustic subsection</span> </button> <ul id="toc-Acoustic-sublist" class="vector-toc-list"> <li id="toc-Automobiles" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Automobiles"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1</span> <span>Automobiles</span> </div> </a> <ul id="toc-Automobiles-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Percussion_instruments" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Percussion_instruments"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2</span> <span>Percussion instruments</span> </div> </a> <ul id="toc-Percussion_instruments-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Stringed_instruments" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Stringed_instruments"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.3</span> <span>Stringed instruments</span> </div> </a> <ul id="toc-Stringed_instruments-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References_and_notes" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References_and_notes"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>References and notes</span> </div> </a> <ul id="toc-References_and_notes-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>External links</span> </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" title="Table of Contents" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Toggle the table of contents</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Resonator</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another 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Available in 28 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-28" 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">28 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%B1%D9%86%D8%A7%D9%86" title="رنان – Arabic" lang="ar" hreflang="ar" data-title="رنان" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%A0%D1%8D%D0%B7%D0%B0%D0%BD%D0%B0%D1%82%D0%B0%D1%80" title="Рэзанатар – Belarusian" lang="be" hreflang="be" data-title="Рэзанатар" data-language-autonym="Беларуская" data-language-local-name="Belarusian" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Ressonador" title="Ressonador – Catalan" lang="ca" hreflang="ca" data-title="Ressonador" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%A0%D0%B5%D0%B7%D0%BE%D0%BD%D0%B0%D1%82%D0%BE%D1%80" title="Резонатор – Chuvash" lang="cv" hreflang="cv" data-title="Резонатор" data-language-autonym="Чӑвашла" data-language-local-name="Chuvash" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Resonator" title="Resonator – German" lang="de" hreflang="de" data-title="Resonator" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Resonaator" title="Resonaator – Estonian" lang="et" hreflang="et" data-title="Resonaator" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%91%CE%BD%CF%84%CE%B7%CF%87%CE%B5%CE%AF%CE%BF" title="Αντηχείο – Greek" lang="el" hreflang="el" data-title="Αντηχείο" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Resonador" title="Resonador – Spanish" lang="es" hreflang="es" data-title="Resonador" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%AA%D8%B4%D8%AF%DB%8C%D8%AF%DA%AF%D8%B1" title="تشدیدگر – Persian" lang="fa" hreflang="fa" data-title="تشدیدگر" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EA%B3%B5%EB%AA%85%EA%B8%B0" title="공명기 – Korean" lang="ko" hreflang="ko" data-title="공명기" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%8C%D5%A5%D5%A6%D5%B8%D5%B6%D5%A1%D5%BF%D5%B8%D6%80" title="Ռեզոնատոր – Armenian" lang="hy" hreflang="hy" data-title="Ռեզոնատոր" data-language-autonym="Հայերեն" data-language-local-name="Armenian" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%85%E0%A4%A8%E0%A5%81%E0%A4%A8%E0%A4%BE%E0%A4%A6%E0%A4%95" title="अनुनादक – Hindi" lang="hi" hreflang="hi" data-title="अनुनादक" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Risuonatore" title="Risuonatore – Italian" lang="it" hreflang="it" data-title="Risuonatore" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%A0%D0%B5%D0%B7%D0%BE%D0%BD%D0%B0%D1%82%D0%BE%D1%80" title="Резонатор – Kazakh" lang="kk" hreflang="kk" data-title="Резонатор" data-language-autonym="Қазақша" data-language-local-name="Kazakh" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%A0%D0%B5%D0%B7%D0%BE%D0%BD%D0%B0%D1%82%D0%BE%D1%80" title="Резонатор – Kyrgyz" lang="ky" hreflang="ky" data-title="Резонатор" data-language-autonym="Кыргызча" data-language-local-name="Kyrgyz" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%85%E0%B4%A8%E0%B5%81%E0%B4%A8%E0%B4%BE%E0%B4%A6%E0%B4%95%E0%B4%82" title="അനുനാദകം – Malayalam" lang="ml" hreflang="ml" data-title="അനുനാദകം" data-language-autonym="മലയാളം" data-language-local-name="Malayalam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E5%85%B1%E6%8C%AF%E5%99%A8" title="共振器 – Japanese" lang="ja" hreflang="ja" data-title="共振器" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Resonator" title="Resonator – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Resonator" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Resonator" title="Resonator – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Resonator" data-language-autonym="Norsk nynorsk" data-language-local-name="Norwegian Nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Rezonator" title="Rezonator – Polish" lang="pl" hreflang="pl" data-title="Rezonator" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Ressonador" title="Ressonador – Portuguese" lang="pt" hreflang="pt" data-title="Ressonador" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%A0%D0%B5%D0%B7%D0%BE%D0%BD%D0%B0%D1%82%D0%BE%D1%80" title="Резонатор – Russian" lang="ru" hreflang="ru" data-title="Резонатор" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Resonator" title="Resonator – Simple English" lang="en-simple" hreflang="en-simple" data-title="Resonator" 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-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Rezonator" title="Rezonator – Serbo-Croatian" lang="sh" hreflang="sh" data-title="Rezonator" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Serbo-Croatian" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Resonaattori" title="Resonaattori – Finnish" lang="fi" hreflang="fi" data-title="Resonaattori" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%92%E0%AE%A4%E0%AF%8D%E0%AE%A4%E0%AE%A4%E0%AE%BF%E0%AE%B0%E0%AF%8D%E0%AE%B5%E0%AE%BF" title="ஒத்ததிர்வி – Tamil" lang="ta" hreflang="ta" data-title="ஒத்ததிர்வி" data-language-autonym="தமிழ்" data-language-local-name="Tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%A0%D0%B5%D0%B7%D0%BE%D0%BD%D0%B0%D1%82%D0%BE%D1%80" title="Резонатор – Ukrainian" lang="uk" hreflang="uk" data-title="Резонатор" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D8%A7%D8%B5%D8%AF%D8%A7%D8%A1_%D8%B3%D8%A7%D8%B2" title="اصداء ساز – Urdu" lang="ur" hreflang="ur" data-title="اصداء ساز" data-language-autonym="اردو" data-language-local-name="Urdu" class="interlanguage-link-target"><span>اردو</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q349669#sitelinks-wikipedia" title="Edit interlanguage links" class="wbc-editpage">Edit links</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Namespaces"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Resonator" 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class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">From Wikipedia, the free encyclopedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Device or system that exhibits resonance</div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">For other uses, see <a href="/wiki/Resonator_(disambiguation)" class="mw-disambig" title="Resonator (disambiguation)">Resonator (disambiguation)</a>.</div> <style data-mw-deduplicate="TemplateStyles:r1251242444">.mw-parser-output .ambox{border:1px solid #a2a9b1;border-left:10px solid #36c;background-color:#fbfbfb;box-sizing:border-box}.mw-parser-output .ambox+link+.ambox,.mw-parser-output .ambox+link+style+.ambox,.mw-parser-output .ambox+link+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+style+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+link+.ambox{margin-top:-1px}html body.mediawiki .mw-parser-output .ambox.mbox-small-left{margin:4px 1em 4px 0;overflow:hidden;width:238px;border-collapse:collapse;font-size:88%;line-height:1.25em}.mw-parser-output .ambox-speedy{border-left:10px solid #b32424;background-color:#fee7e6}.mw-parser-output .ambox-delete{border-left:10px solid #b32424}.mw-parser-output .ambox-content{border-left:10px solid #f28500}.mw-parser-output .ambox-style{border-left:10px solid #fc3}.mw-parser-output .ambox-move{border-left:10px solid #9932cc}.mw-parser-output .ambox-protection{border-left:10px solid #a2a9b1}.mw-parser-output .ambox .mbox-text{border:none;padding:0.25em 0.5em;width:100%}.mw-parser-output .ambox .mbox-image{border:none;padding:2px 0 2px 0.5em;text-align:center}.mw-parser-output .ambox .mbox-imageright{border:none;padding:2px 0.5em 2px 0;text-align:center}.mw-parser-output .ambox .mbox-empty-cell{border:none;padding:0;width:1px}.mw-parser-output .ambox .mbox-image-div{width:52px}@media(min-width:720px){.mw-parser-output .ambox{margin:0 10%}}@media print{body.ns-0 .mw-parser-output .ambox{display:none!important}}</style><table class="box-More_citations_needed plainlinks metadata ambox ambox-content ambox-Refimprove" role="presentation"><tbody><tr><td class="mbox-image"><div class="mbox-image-div"><span typeof="mw:File"><a href="/wiki/File:Question_book-new.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/50px-Question_book-new.svg.png" decoding="async" width="50" height="39" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/75px-Question_book-new.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/100px-Question_book-new.svg.png 2x" data-file-width="512" data-file-height="399" /></a></span></div></td><td class="mbox-text"><div class="mbox-text-span">This article <b>needs additional citations for <a href="/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability">verification</a></b>.<span class="hide-when-compact"> Please help <a href="/wiki/Special:EditPage/Resonator" title="Special:EditPage/Resonator">improve this article</a> by <a href="/wiki/Help:Referencing_for_beginners" title="Help:Referencing for beginners">adding citations to reliable sources</a>. Unsourced material may be challenged and removed.<br /><small><span class="plainlinks"><i>Find sources:</i> <a rel="nofollow" class="external text" href="https://www.google.com/search?as_eq=wikipedia&q=%22Resonator%22">"Resonator"</a> – <a rel="nofollow" class="external text" href="https://www.google.com/search?tbm=nws&q=%22Resonator%22+-wikipedia&tbs=ar:1">news</a> <b>·</b> <a rel="nofollow" class="external text" href="https://www.google.com/search?&q=%22Resonator%22&tbs=bkt:s&tbm=bks">newspapers</a> <b>·</b> <a rel="nofollow" class="external text" href="https://www.google.com/search?tbs=bks:1&q=%22Resonator%22+-wikipedia">books</a> <b>·</b> <a rel="nofollow" class="external text" href="https://scholar.google.com/scholar?q=%22Resonator%22">scholar</a> <b>·</b> <a rel="nofollow" class="external text" href="https://www.jstor.org/action/doBasicSearch?Query=%22Resonator%22&acc=on&wc=on">JSTOR</a></span></small></span> <span class="date-container"><i>(<span class="date">January 2008</span>)</i></span><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> <p>A <b>resonator</b> is a device or system that exhibits <a href="/wiki/Resonance" title="Resonance">resonance</a> or resonant behavior. That is, it naturally <a href="/wiki/Oscillation" title="Oscillation">oscillates</a> with greater <a href="/wiki/Amplitude" title="Amplitude">amplitude</a> at some <a href="/wiki/Frequency" title="Frequency">frequencies</a>, called <a href="/wiki/Resonance_frequency" class="mw-redirect" title="Resonance frequency">resonant frequencies</a>, than at other frequencies. The oscillations in a resonator can be either <a href="/wiki/Electromagnetic_radiation" title="Electromagnetic radiation">electromagnetic</a> or mechanical (including <a href="/wiki/Acoustics" title="Acoustics">acoustic</a>). Resonators are used to either generate waves of specific frequencies or to select specific frequencies from a signal. Musical instruments use <a href="/wiki/Musical_acoustics" title="Musical acoustics">acoustic</a> resonators that produce sound waves of specific tones. Another example is <a href="/wiki/Crystal_oscillator" title="Crystal oscillator">quartz crystals</a> used in electronic devices such as <a href="/wiki/Radio_transmitter" class="mw-redirect" title="Radio transmitter">radio transmitters</a> and <a href="/wiki/Quartz_clock" title="Quartz clock">quartz watches</a> to produce oscillations of very precise frequency. </p> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Two_dim_standing_wave.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/ac/Two_dim_standing_wave.gif/130px-Two_dim_standing_wave.gif" decoding="async" width="130" height="91" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/ac/Two_dim_standing_wave.gif/195px-Two_dim_standing_wave.gif 1.5x, //upload.wikimedia.org/wikipedia/commons/a/ac/Two_dim_standing_wave.gif 2x" data-file-width="200" data-file-height="140" /></a><figcaption>A standing wave in a rectangular cavity resonator</figcaption></figure> <p>A <b>cavity resonator</b> is one in which waves exist in a hollow space inside the device. In electronics and radio, <a href="/wiki/Microwave_cavity" title="Microwave cavity">microwave cavities</a> consisting of hollow metal boxes are used in microwave transmitters, receivers and test equipment to control frequency, in place of the <a href="/wiki/Tuned_circuit" class="mw-redirect" title="Tuned circuit">tuned circuits</a> which are used at lower frequencies. Acoustic cavity resonators, in which sound is produced by air vibrating in a cavity with one opening, are known as <a href="/wiki/Helmholtz_resonance" title="Helmholtz resonance">Helmholtz resonators</a>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Explanation">Explanation</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Resonator&action=edit&section=1" title="Edit section: Explanation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A physical system can have as many <a href="/wiki/Resonant_frequency" class="mw-redirect" title="Resonant frequency">resonant frequencies</a> as it has <a href="/wiki/Degrees_of_freedom_(engineering)" class="mw-redirect" title="Degrees of freedom (engineering)">degrees of freedom</a>; each degree of freedom can vibrate as a <a href="/wiki/Harmonic_oscillator" title="Harmonic oscillator">harmonic oscillator</a>. Systems with one degree of freedom, such as a mass on a spring, <a href="/wiki/Pendulum" title="Pendulum">pendulums</a>, <a href="/wiki/Balance_wheel" title="Balance wheel">balance wheels</a>, and <a href="/wiki/RLC_circuit" title="RLC circuit">LC tuned circuits</a> have one resonant frequency. Systems with two degrees of freedom, such as <a href="/wiki/Double_pendulum" title="Double pendulum">coupled pendulums</a> and <a href="/wiki/Transformer" title="Transformer">resonant transformers</a> can have two resonant frequencies. A <a href="/wiki/Crystal_lattice" class="mw-redirect" title="Crystal lattice">crystal lattice</a> composed of <i>N</i> atoms bound together can have <i>N</i> resonant frequencies. As the number of coupled harmonic oscillators grows, the time it takes to transfer energy from one to the next becomes significant. The vibrations in them begin to travel through the coupled harmonic oscillators in waves, from one oscillator to the next. </p><p>The term <i>resonator</i> is most often used for a homogeneous object in which vibrations travel as waves, at an approximately constant velocity, bouncing back and forth between the sides of the resonator. The material of the resonator, through which the waves flow, can be viewed as being made of millions of coupled moving parts (such as atoms). Therefore, they can have millions of resonant frequencies, although only a few may be used in practical resonators. The oppositely moving waves <a href="/wiki/Interference_(physics)" class="mw-redirect" title="Interference (physics)">interfere</a> with each other, and at its <a href="/wiki/Resonant_frequency" class="mw-redirect" title="Resonant frequency">resonant frequencies</a> reinforce each other to create a pattern of <a href="/wiki/Standing_wave" title="Standing wave">standing waves</a> in the resonator. If the distance between the sides is <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 d\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle d\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0f203b686a923982358b9274fb508753ac31b996" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.603ex; height:2.176ex;" alt="{\displaystyle d\,}"></span>, the length of a round trip is <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 2d\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>2</mn> <mi>d</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 2d\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ce79e61f06076eb7097dfff220e2b1c76576b165" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.765ex; height:2.176ex;" alt="{\displaystyle 2d\,}"></span>. To cause resonance, the <a href="/wiki/Phase_(waves)" title="Phase (waves)">phase</a> of a <a href="/wiki/Sinusoidal" class="mw-redirect" title="Sinusoidal">sinusoidal</a> wave after a round trip must be equal to the initial phase so the waves self-reinforce. The condition for resonance in a resonator is that the round trip distance, <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 2d\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>2</mn> <mi>d</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 2d\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ce79e61f06076eb7097dfff220e2b1c76576b165" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.765ex; height:2.176ex;" alt="{\displaystyle 2d\,}"></span>, is equal to an integer number of wavelengths <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \lambda \,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>λ</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lambda \,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/988b7b8a22b11081bc97378c30391f573535c21c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.742ex; height:2.176ex;" alt="{\displaystyle \lambda \,}"></span> of the wave: </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 2d=N\lambda ,\qquad \qquad N\in \{1,2,3,\dots \}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>2</mn> <mi>d</mi> <mo>=</mo> <mi>N</mi> <mi>λ</mi> <mo>,</mo> <mspace width="2em" /> <mspace width="2em" /> <mi>N</mi> <mo>∈</mo> <mo fence="false" stretchy="false">{</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mn>3</mn> <mo>,</mo> <mo>…</mo> <mo fence="false" stretchy="false">}</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 2d=N\lambda ,\qquad \qquad N\in \{1,2,3,\dots \}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b353876ae423898b981ff38740b75512d8459349" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:35.762ex; height:2.843ex;" alt="{\displaystyle 2d=N\lambda ,\qquad \qquad N\in \{1,2,3,\dots \}}"></span></dd></dl> <p>If the velocity of a wave is <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> <mspace width="thinmathspace" /> </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/8573e7d95140b0d4068258d8162e189563baee6b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.394ex; height:1.676ex;" alt="{\displaystyle c\,}"></span>, the frequency is <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f=c/\lambda \,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mo>=</mo> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>λ</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f=c/\lambda \,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4ddb81f725ba3b40091fb88bf33a792f243310e7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:8.289ex; height:2.843ex;" alt="{\displaystyle f=c/\lambda \,}"></span> so the resonant frequencies are: </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 f={\frac {Nc}{2d}}\qquad \qquad N\in \{1,2,3,\dots \}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>N</mi> <mi>c</mi> </mrow> <mrow> <mn>2</mn> <mi>d</mi> </mrow> </mfrac> </mrow> <mspace width="2em" /> <mspace width="2em" /> <mi>N</mi> <mo>∈</mo> <mo fence="false" stretchy="false">{</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mn>3</mn> <mo>,</mo> <mo>…</mo> <mo fence="false" stretchy="false">}</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f={\frac {Nc}{2d}}\qquad \qquad N\in \{1,2,3,\dots \}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4300b54567ebab5e2601fc4650653b48b2c4f076" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:34.116ex; height:5.343ex;" alt="{\displaystyle f={\frac {Nc}{2d}}\qquad \qquad N\in \{1,2,3,\dots \}}"></span></dd></dl> <p>So the resonant frequencies of resonators, called <a href="/wiki/Normal_modes" class="mw-redirect" title="Normal modes">normal modes</a>, are equally spaced multiples (<a href="/wiki/Harmonic" title="Harmonic">harmonics</a>) of a lowest frequency called the <a href="/wiki/Fundamental_frequency" title="Fundamental frequency">fundamental frequency</a>. The above analysis assumes the medium inside the resonator is homogeneous, so the waves travel at a constant speed, and that the shape of the resonator is rectilinear. If the resonator is inhomogeneous or has a nonrectilinear shape, like a circular <a href="/wiki/Drum" title="Drum">drumhead</a> or a cylindrical <a href="/wiki/Microwave_cavity" title="Microwave cavity">microwave cavity</a>, the resonant frequencies may not occur at equally spaced multiples of the fundamental frequency. They are then called <a href="/wiki/Overtone" title="Overtone">overtones</a> instead of <a href="/wiki/Harmonic" title="Harmonic">harmonics</a>. There may be several such series of resonant frequencies in a single resonator, corresponding to different modes of vibration. </p> <div class="mw-heading mw-heading2"><h2 id="Electromagnetics">Electromagnetics</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Resonator&action=edit&section=2" title="Edit section: Electromagnetics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol 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phenomena">Phenomena</a></li></ul></td> </tr><tr><td class="sidebar-content hlist"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:transparent;border-top:1px solid #aaa;text-align:center;;color: var(--color-base)"><a href="/wiki/Electrostatics" title="Electrostatics">Electrostatics</a></div><div class="sidebar-list-content mw-collapsible-content hlist"> <ul><li><a href="/wiki/Charge_density" title="Charge density">Charge density</a></li> <li><a href="/wiki/Electrical_conductor" title="Electrical conductor">Conductor</a></li> <li><a href="/wiki/Coulomb%27s_law" title="Coulomb's law">Coulomb law</a></li> <li><a href="/wiki/Electret" title="Electret">Electret</a></li> <li><a href="/wiki/Electric_charge" title="Electric charge">Electric charge</a></li> <li><a href="/wiki/Electric_dipole_moment" title="Electric dipole moment">Electric dipole</a></li> <li><a href="/wiki/Electric_field" title="Electric field">Electric field</a></li> <li><a href="/wiki/Electric_flux" title="Electric flux">Electric flux</a></li> <li><a href="/wiki/Electric_potential" title="Electric potential">Electric potential</a></li> <li><a href="/wiki/Electrostatic_discharge" title="Electrostatic discharge">Electrostatic discharge</a></li> <li><a href="/wiki/Electrostatic_induction" title="Electrostatic induction">Electrostatic induction</a></li> <li><a href="/wiki/Gauss%27s_law" title="Gauss's law">Gauss law</a></li> <li><a href="/wiki/Insulator_(electricity)" title="Insulator (electricity)">Insulator</a></li> <li><a href="/wiki/Permittivity" title="Permittivity">Permittivity</a></li> <li><a href="/wiki/Polarization_density" title="Polarization density">Polarization</a></li> <li><a href="/wiki/Electric_potential_energy" title="Electric potential energy">Potential energy</a></li> <li><a href="/wiki/Static_electricity" title="Static electricity">Static electricity</a></li> <li><a href="/wiki/Triboelectric_effect" title="Triboelectric effect">Triboelectricity</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content hlist"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:transparent;border-top:1px solid #aaa;text-align:center;;color: var(--color-base)"><a href="/wiki/Magnetostatics" title="Magnetostatics">Magnetostatics</a></div><div class="sidebar-list-content mw-collapsible-content hlist"> <ul><li><a href="/wiki/Amp%C3%A8re%27s_circuital_law" title="Ampère's circuital law">Ampère law</a></li> <li><a href="/wiki/Biot%E2%80%93Savart_law" title="Biot–Savart law">Biot–Savart law</a></li> <li><a href="/wiki/Gauss%27s_law_for_magnetism" title="Gauss's law for magnetism">Gauss magnetic law</a></li> <li><a href="/wiki/Magnetic_moment" title="Magnetic moment">Magnetic dipole</a></li> <li><a href="/wiki/Magnetic_field" title="Magnetic field">Magnetic field</a></li> <li><a href="/wiki/Magnetic_flux" title="Magnetic flux">Magnetic flux</a></li> <li><a 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title="Bremsstrahlung">Bremsstrahlung</a></li> <li><a href="/wiki/Cyclotron_radiation" title="Cyclotron radiation">Cyclotron radiation</a></li> <li><a href="/wiki/Displacement_current" title="Displacement current">Displacement current</a></li> <li><a href="/wiki/Eddy_current" title="Eddy current">Eddy current</a></li> <li><a href="/wiki/Electromagnetic_field" title="Electromagnetic field">Electromagnetic field</a></li> <li><a href="/wiki/Electromagnetic_induction" title="Electromagnetic induction">Electromagnetic induction</a></li> <li><a href="/wiki/Electromagnetic_pulse" title="Electromagnetic pulse">Electromagnetic pulse</a></li> <li><a href="/wiki/Electromagnetic_radiation" title="Electromagnetic radiation">Electromagnetic radiation</a></li> <li><a href="/wiki/Faraday%27s_law_of_induction" title="Faraday's law of induction">Faraday law</a></li> <li><a href="/wiki/Jefimenko%27s_equations" title="Jefimenko's equations">Jefimenko equations</a></li> <li><a href="/wiki/Larmor_formula" title="Larmor formula">Larmor formula</a></li> <li><a href="/wiki/Lenz%27s_law" title="Lenz's law">Lenz law</a></li> <li><a href="/wiki/Li%C3%A9nard%E2%80%93Wiechert_potential" title="Liénard–Wiechert potential">Liénard–Wiechert potential</a></li> <li><a href="/wiki/London_equations" title="London equations">London equations</a></li> <li><a href="/wiki/Lorentz_force" title="Lorentz force">Lorentz force</a></li> <li><a href="/wiki/Maxwell%27s_equations" title="Maxwell's equations">Maxwell equations</a></li> <li><a href="/wiki/Maxwell_stress_tensor" title="Maxwell stress tensor">Maxwell tensor</a></li> <li><a href="/wiki/Poynting_vector" title="Poynting vector">Poynting vector</a></li> <li><a href="/wiki/Synchrotron_radiation" title="Synchrotron radiation">Synchrotron radiation</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content hlist"> <div class="sidebar-list mw-collapsible"><div class="sidebar-list-title" style="background:transparent;border-top:1px solid 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href="/wiki/Inductance" title="Inductance">Inductance</a></li> <li><a href="/wiki/Joule_heating" title="Joule heating">Joule heating</a></li> <li><a href="/wiki/Kirchhoff%27s_circuit_laws" title="Kirchhoff's circuit laws">Kirchhoff laws</a></li> <li><a href="/wiki/Network_analysis_(electrical_circuits)" title="Network analysis (electrical circuits)">Network analysis</a></li> <li><a href="/wiki/Ohm%27s_law" title="Ohm's law">Ohm law</a></li> <li><a href="/wiki/Series_and_parallel_circuits#Parallel_circuits" title="Series and parallel circuits">Parallel circuit</a></li> <li><a href="/wiki/Electrical_resistance_and_conductance" title="Electrical resistance and conductance">Resistance</a></li> <li><a class="mw-selflink-fragment" href="#Electromagnetics">Resonant cavities</a></li> <li><a href="/wiki/Series_and_parallel_circuits#Series_circuits" title="Series and parallel circuits">Series circuit</a></li> <li><a href="/wiki/Voltage" title="Voltage">Voltage</a></li> <li><a href="/wiki/Watt" title="Watt">Watt</a></li> <li><a href="/wiki/Waveguide_(radio_frequency)" title="Waveguide (radio frequency)">Waveguides</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content hlist"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:transparent;border-top:1px solid #aaa;text-align:center;;color: var(--color-base)"><a href="/wiki/Magnetic_circuit" title="Magnetic circuit">Magnetic circuit</a></div><div class="sidebar-list-content mw-collapsible-content hlist"> <ul><li><a href="/wiki/AC_motor" title="AC motor">AC motor</a></li> <li><a href="/wiki/DC_motor" title="DC motor">DC motor</a></li> <li><a href="/wiki/Electric_machine" title="Electric machine">Electric machine</a></li> <li><a href="/wiki/Electric_motor" title="Electric motor">Electric motor</a></li> <li><a href="/wiki/Gyrator%E2%80%93capacitor_model" title="Gyrator–capacitor model">Gyrator–capacitor</a></li> <li><a href="/wiki/Induction_motor" title="Induction motor">Induction motor</a></li> <li><a href="/wiki/Linear_motor" title="Linear motor">Linear motor</a></li> <li><a href="/wiki/Magnetomotive_force" title="Magnetomotive force">Magnetomotive force</a></li> <li><a href="/wiki/Permeance" title="Permeance">Permeance</a></li> <li><a href="/wiki/Magnetic_complex_reluctance" title="Magnetic complex reluctance">Reluctance (complex)</a></li> <li><a href="/wiki/Magnetic_reluctance" title="Magnetic reluctance">Reluctance (real)</a></li> <li><a href="/wiki/Rotor_(electric)" title="Rotor (electric)">Rotor</a></li> <li><a href="/wiki/Stator" title="Stator">Stator</a></li> <li><a href="/wiki/Transformer" title="Transformer">Transformer</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content hlist"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:transparent;border-top:1px solid #aaa;text-align:center;;color: var(--color-base)"><a href="/wiki/Covariant_formulation_of_classical_electromagnetism" title="Covariant formulation of classical electromagnetism">Covariant formulation</a></div><div class="sidebar-list-content mw-collapsible-content hlist"> <ul><li><a href="/wiki/Electromagnetic_tensor" title="Electromagnetic tensor">Electromagnetic tensor</a></li> <li><a href="/wiki/Classical_electromagnetism_and_special_relativity" title="Classical electromagnetism and special relativity">Electromagnetism and special relativity</a></li> <li><a href="/wiki/Four-current" title="Four-current">Four-current</a></li> <li><a href="/wiki/Electromagnetic_four-potential" title="Electromagnetic four-potential">Four-potential</a></li> <li><a href="/wiki/Mathematical_descriptions_of_the_electromagnetic_field" title="Mathematical descriptions of the electromagnetic field">Mathematical descriptions</a></li> <li><a href="/wiki/Maxwell%27s_equations_in_curved_spacetime" title="Maxwell's equations in curved spacetime">Maxwell equations in curved spacetime</a></li> <li><a href="/wiki/Relativistic_electromagnetism" title="Relativistic electromagnetism">Relativistic electromagnetism</a></li> <li><a href="/wiki/Electromagnetic_stress%E2%80%93energy_tensor" title="Electromagnetic stress–energy tensor">Stress–energy tensor</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content hlist"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="background:transparent;border-top:1px solid #aaa;text-align:center;;color: var(--color-base)">Scientists</div><div class="sidebar-list-content mw-collapsible-content hlist"> <ul><li><a href="/wiki/Andr%C3%A9-Marie_Amp%C3%A8re" title="André-Marie Ampère">Ampère</a></li> <li><a href="/wiki/Jean-Baptiste_Biot" title="Jean-Baptiste Biot">Biot</a></li> <li><a href="/wiki/Charles-Augustin_de_Coulomb" title="Charles-Augustin de Coulomb">Coulomb</a></li> <li><a href="/wiki/Humphry_Davy" title="Humphry Davy">Davy</a></li> <li><a href="/wiki/Albert_Einstein" title="Albert Einstein">Einstein</a></li> <li><a href="/wiki/Michael_Faraday" title="Michael Faraday">Faraday</a></li> <li><a href="/wiki/Hippolyte_Fizeau" title="Hippolyte Fizeau">Fizeau</a></li> <li><a href="/wiki/Carl_Friedrich_Gauss" title="Carl Friedrich Gauss">Gauss</a></li> <li><a href="/wiki/Oliver_Heaviside" title="Oliver Heaviside">Heaviside</a></li> <li><a href="/wiki/Hermann_von_Helmholtz" title="Hermann von Helmholtz">Helmholtz</a></li> <li><a href="/wiki/Joseph_Henry" title="Joseph Henry">Henry</a></li> <li><a href="/wiki/Heinrich_Hertz" title="Heinrich Hertz">Hertz</a></li> <li><a href="/wiki/John_Hopkinson" title="John Hopkinson">Hopkinson</a></li> <li><a href="/wiki/Oleg_D._Jefimenko" title="Oleg D. Jefimenko">Jefimenko</a></li> <li><a href="/wiki/James_Prescott_Joule" title="James Prescott Joule">Joule</a></li> <li><a href="/wiki/Lord_Kelvin" title="Lord Kelvin">Kelvin</a></li> <li><a href="/wiki/Gustav_Kirchhoff" title="Gustav Kirchhoff">Kirchhoff</a></li> <li><a href="/wiki/Joseph_Larmor" title="Joseph Larmor">Larmor</a></li> <li><a href="/wiki/Emil_Lenz" title="Emil Lenz">Lenz</a></li> <li><a href="/wiki/Alfred-Marie_Li%C3%A9nard" title="Alfred-Marie Liénard">Liénard</a></li> <li><a href="/wiki/Hendrik_Lorentz" title="Hendrik Lorentz">Lorentz</a></li> <li><a href="/wiki/James_Clerk_Maxwell" title="James Clerk Maxwell">Maxwell</a></li> <li><a href="/wiki/Franz_Ernst_Neumann" title="Franz Ernst Neumann">Neumann</a></li> <li><a href="/wiki/Georg_Ohm" title="Georg Ohm">Ohm</a></li> <li><a href="/wiki/Hans_Christian_%C3%98rsted" title="Hans Christian Ørsted">Ørsted</a></li> <li><a href="/wiki/Sim%C3%A9on_Denis_Poisson" title="Siméon Denis Poisson">Poisson</a></li> <li><a href="/wiki/John_Henry_Poynting" title="John Henry Poynting">Poynting</a></li> <li><a href="/wiki/William_Ritchie_(physicist)" title="William Ritchie (physicist)">Ritchie</a></li> <li><a href="/wiki/F%C3%A9lix_Savart" title="Félix Savart">Savart</a></li> <li><a href="/wiki/George_Singer" title="George Singer">Singer</a></li> <li><a href="/wiki/Charles_Proteus_Steinmetz" title="Charles Proteus Steinmetz">Steinmetz</a></li> <li><a href="/wiki/Nikola_Tesla" title="Nikola Tesla">Tesla</a></li> <li><a href="/wiki/J._J._Thomson" title="J. J. Thomson">Thomson</a></li> <li><a href="/wiki/Alessandro_Volta" title="Alessandro Volta">Volta</a></li> <li><a href="/wiki/Wilhelm_Eduard_Weber" title="Wilhelm Eduard Weber">Weber</a></li> <li><a href="/wiki/Emil_Wiechert" title="Emil Wiechert">Wiechert</a></li></ul></div></div></td> </tr><tr><td class="sidebar-navbar"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1239400231">.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}html.skin-theme-clientpref-night .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Electromagnetism" title="Template:Electromagnetism"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Electromagnetism" title="Template talk:Electromagnetism"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Electromagnetism" title="Special:EditPage/Template:Electromagnetism"><abbr title="Edit this template">e</abbr></a></li></ul></div></td></tr></tbody></table> <div class="mw-heading mw-heading3"><h3 id="Resonant_circuits">Resonant circuits</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Resonator&action=edit&section=3" title="Edit section: Resonant circuits"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Electrical_resonance" title="Electrical resonance">electrical resonance</a></div> <p>An electrical circuit composed of discrete components can act as a resonator when both an <a href="/wiki/Inductor" title="Inductor">inductor</a> and <a href="/wiki/Capacitor" title="Capacitor">capacitor</a> are included. Oscillations are limited by the inclusion of resistance, either via a specific <a href="/wiki/Resistor" title="Resistor">resistor</a> component, or due to <a href="/wiki/Electrical_resistance" class="mw-redirect" title="Electrical resistance">resistance</a> of the inductor windings. Such <a href="/wiki/Resonant_circuit" class="mw-redirect" title="Resonant circuit">resonant circuits</a> are also called <a href="/wiki/RLC_circuit" title="RLC circuit">RLC circuits</a> after the circuit symbols for the components. </p><p>A <a href="/wiki/Distributed-element_model" title="Distributed-element model">distributed-parameter</a> resonator has capacitance, inductance, and resistance that cannot be isolated into separate lumped capacitors, inductors, or resistors. An example of this, much used in <a href="/wiki/Filter_(signal_processing)" title="Filter (signal processing)">filtering</a>, is the <a href="/wiki/Helical_resonator" title="Helical resonator">helical resonator</a>. </p><p>An <a href="/wiki/Inductor" title="Inductor">inductor</a> consisting of a coil of wire, is self-resonant at a certain frequency due to the <a href="/wiki/Parasitic_capacitance" title="Parasitic capacitance">parasitic capacitance</a> between its turns. This is often an unwanted effect that can cause <a href="/wiki/Parasitic_oscillation" title="Parasitic oscillation">parasitic oscillations</a> in RF circuits. The self-resonance of inductors is used in a few circuits, such as the <a href="/wiki/Tesla_coil" title="Tesla coil">Tesla coil</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Cavity_resonators">Cavity resonators</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Resonator&action=edit&section=4" title="Edit section: Cavity resonators"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Microwave_cavity" title="Microwave cavity">Microwave cavity</a></div> <p>A <i>cavity resonator</i> is a hollow closed conductor such as a metal box or a cavity within a metal block, containing <a href="/wiki/Electromagnetic_wave" class="mw-redirect" title="Electromagnetic wave">electromagnetic waves</a> (radio waves) reflecting back and forth between the cavity's walls. When a source of radio waves at one of the cavity's <a href="/wiki/Resonant_frequency" class="mw-redirect" title="Resonant frequency">resonant frequencies</a> is applied, the oppositely-moving waves form <a href="/wiki/Standing_wave" title="Standing wave">standing waves</a>, and the cavity stores electromagnetic energy. </p><p>Since the cavity's lowest resonant frequency, the fundamental frequency, is that at which the width of the cavity is equal to a half-wavelength (λ/2), cavity resonators are only used at <a href="/wiki/Microwave" title="Microwave">microwave</a> frequencies and above, where wavelengths are short enough that the cavity is conveniently small in size. </p><p>Due to the low resistance of their conductive walls, cavity resonators have very high <a href="/wiki/Q_factor" title="Q factor">Q factors</a>; that is their <a href="/wiki/Bandwidth_(signal_processing)" title="Bandwidth (signal processing)">bandwidth</a>, the range of frequencies around the resonant frequency at which they will resonate, is very narrow. Thus they can act as narrow <a href="/wiki/Bandpass_filter" class="mw-redirect" title="Bandpass filter">bandpass filters</a>. Cavity resonators are widely used as the frequency determining element in <a href="/wiki/Electronic_oscillator" title="Electronic oscillator">microwave oscillators</a>. Their resonant frequency can be tuned by moving one of the walls of the cavity in or out, changing its size. </p> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:US_Patent_2424267_Figs_1a,_1b,_1c.PNG" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/a/a2/US_Patent_2424267_Figs_1a%2C_1b%2C_1c.PNG" decoding="async" width="206" height="390" class="mw-file-element" data-file-width="206" data-file-height="390" /></a><figcaption>An illustration of the electric and magnetic field of one of the possible modes in a cavity resonator.</figcaption></figure> <div class="mw-heading mw-heading4"><h4 id="Cavity_magnetron">Cavity magnetron</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Resonator&action=edit&section=5" title="Edit section: Cavity magnetron"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Cavity_magnetron" title="Cavity magnetron">cavity magnetron</a></div> <p>The <a href="/wiki/Cavity_magnetron" title="Cavity magnetron">cavity magnetron</a> is a vacuum tube with a filament in the center of an evacuated, lobed, circular cavity resonator. A perpendicular magnetic field is imposed by a permanent magnet. The magnetic field causes the electrons, attracted to the (relatively) positive outer part of the chamber, to spiral outward in a circular path rather than moving directly to this anode. Spaced about the rim of the chamber are cylindrical cavities. The cavities are open along their length and so they connect with the common cavity space. As electrons sweep past these openings they induce a resonant high frequency radio field in the cavity, which in turn causes the electrons to bunch into groups. A portion of this field is extracted with a short antenna that is connected to a waveguide (a metal tube usually of rectangular cross section). The <a href="/wiki/Waveguide" title="Waveguide">waveguide</a> directs the extracted RF energy to the load, which may be a cooking chamber in a microwave oven or a high gain antenna in the case of radar. </p> <div class="mw-heading mw-heading4"><h4 id="Klystron">Klystron</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Resonator&action=edit&section=6" title="Edit section: Klystron"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Klystron" title="Klystron">klystron</a></div> <p>The <a href="/wiki/Klystron" title="Klystron">klystron</a>, tube waveguide, is a beam tube including at least two apertured cavity resonators. The beam of charged particles passes through the apertures of the resonators, often tunable wave reflection grids, in succession. A collector electrode is provided to intercept the beam after passing through the resonators. The first resonator causes bunching of the particles passing through it. The bunched particles travel in a field-free region where further bunching occurs, then the bunched particles enter the second resonator giving up their energy to excite it into oscillations. It is a <a href="/wiki/Particle_accelerator" title="Particle accelerator">particle accelerator</a> that works in conjunction with a specifically tuned cavity by the configuration of the structures. </p><p>The <a href="/wiki/Reflex_klystron" class="mw-redirect" title="Reflex klystron">reflex klystron</a> is a klystron utilizing only a single apertured cavity resonator through which the beam of charged particles passes, first in one direction. A repeller electrode is provided to repel (or redirect) the beam after passage through the resonator back through the resonator in the other direction and in proper phase to reinforce the oscillations set up in the resonator. </p> <figure class="mw-default-size mw-halign-left" typeof="mw:File/Thumb"><a href="/wiki/File:Aust.-Synchrotron,-RF-Cavities-of-Linac-(Bunchers),-14.06.2007.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/fe/Aust.-Synchrotron%2C-RF-Cavities-of-Linac-%28Bunchers%29%2C-14.06.2007.jpg/220px-Aust.-Synchrotron%2C-RF-Cavities-of-Linac-%28Bunchers%29%2C-14.06.2007.jpg" decoding="async" width="220" height="165" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/fe/Aust.-Synchrotron%2C-RF-Cavities-of-Linac-%28Bunchers%29%2C-14.06.2007.jpg/330px-Aust.-Synchrotron%2C-RF-Cavities-of-Linac-%28Bunchers%29%2C-14.06.2007.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/fe/Aust.-Synchrotron%2C-RF-Cavities-of-Linac-%28Bunchers%29%2C-14.06.2007.jpg/440px-Aust.-Synchrotron%2C-RF-Cavities-of-Linac-%28Bunchers%29%2C-14.06.2007.jpg 2x" data-file-width="1200" data-file-height="900" /></a><figcaption>RF cavities in the <a href="/wiki/Linear_particle_accelerator" title="Linear particle accelerator">linac</a> of the <a href="/wiki/Australian_Synchrotron" title="Australian Synchrotron">Australian Synchrotron</a> are used to accelerate and bunch beams of <a href="/wiki/Electron" title="Electron">electrons</a>; the linac is the tube passing through the middle of the cavity.</figcaption></figure> <div class="mw-heading mw-heading4"><h4 id="Application_in_particle_accelerators">Application in particle accelerators</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Resonator&action=edit&section=7" title="Edit section: Application in particle accelerators"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>On the <a href="/wiki/Beamline" title="Beamline">beamline</a> of an accelerator system, there are specific sections that are cavity resonators for <a href="/wiki/Radio_frequency" title="Radio frequency">radio frequency</a> (RF) radiation. The (charged) particles that are to be accelerated pass through these cavities in such a way that the microwave electric field transfers energy to the particles, thus increasing their kinetic energy and thus accelerating them. Several large accelerator facilities employ <a href="/wiki/Superconducting_radio_frequency" title="Superconducting radio frequency">superconducting niobium cavities</a> for improved performance compared to metallic (copper) cavities. </p> <div class="mw-heading mw-heading3"><h3 id="Loop-gap_resonator">Loop-gap resonator</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Resonator&action=edit&section=8" title="Edit section: Loop-gap resonator"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Loop-gap_resonator" title="Loop-gap resonator">loop-gap resonator</a></div> <p>The <a href="/wiki/Loop-gap_resonator" title="Loop-gap resonator">loop-gap resonator</a> (LGR) is made by cutting a narrow slit along the length of a conducting tube. The slit has an effective capacitance and the bore of the resonator has an effective inductance. Therefore, the LGR can be modeled as an RLC circuit and has a resonant frequency that is typically between 200 MHz and 2 GHz. In the absence of radiation losses, the effective resistance of the LGR is determined by the resistivity and electromagnetic skin depth of the conductor used to make the resonator. </p><p>One key advantage of the LGR is that, at its resonant frequency, its dimensions are small compared to the free-space wavelength of the electromagnetic fields. Therefore, it is possible to use LGRs to construct a compact and high-Q resonator that operates at relatively low frequencies where cavity resonators would be impractically large. </p> <div class="mw-heading mw-heading3"><h3 id="Dielectric_resonators">Dielectric resonators</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Resonator&action=edit&section=9" title="Edit section: Dielectric resonators"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Dielectric_resonator" title="Dielectric resonator">Dielectric resonator</a></div> <p>If a piece of material with large dielectric constant is surrounded by a material with much lower dielectric constant, then this abrupt change in dielectric constant can cause confinement of an electromagnetic wave, which leads to a resonator that acts similarly to a cavity resonator.<sup id="cite_ref-pozar_1-0" class="reference"><a href="#cite_note-pozar-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Transmission-line_resonators">Transmission-line resonators</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Resonator&action=edit&section=10" title="Edit section: Transmission-line resonators"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Transmission_line" title="Transmission line">Transmission lines</a> are structures that allow broadband transmission of electromagnetic waves, e.g. at radio or microwave frequencies. Abrupt change of impedance (e.g. open or short) in a transmission line causes reflection of the transmitted signal. Two such reflectors on a transmission line evoke standing waves between them and thus act as a one-dimensional resonator, with the resonance frequencies determined by their distance and the effective dielectric constant of the transmission line.<sup id="cite_ref-pozar_1-1" class="reference"><a href="#cite_note-pozar-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> A common form is the <a href="/wiki/Resonant_stub" class="mw-redirect" title="Resonant stub">resonant stub</a>, a length of transmission line terminated in either a <a href="/wiki/Short_circuit" title="Short circuit">short circuit</a> or open circuit, connected in series or parallel with a main transmission line. </p><p>Planar transmission-line resonators are commonly employed for <a href="/wiki/Coplanar_waveguide" title="Coplanar waveguide">coplanar</a>, <a href="/wiki/Stripline" title="Stripline">stripline</a>, and <a href="/wiki/Microstrip" title="Microstrip">microstrip</a> transmission lines. Such planar transmission-line resonators can be very compact in size and are widely used elements in microwave circuitry. In cryogenic solid-state research, superconducting transmission-line resonators contribute to solid-state spectroscopy <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> and quantum information science.<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><sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Optical_cavities">Optical cavities</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Resonator&action=edit&section=11" title="Edit section: Optical cavities"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In a <a href="/wiki/Laser" title="Laser">laser</a>, light is amplified in a cavity resonator that is usually composed of two or more mirrors. Thus an <i><a href="/wiki/Optical_cavity" title="Optical cavity">optical cavity</a></i>, also known as a resonator, is a cavity with walls that reflect <a href="/wiki/Electromagnetic_waves" class="mw-redirect" title="Electromagnetic waves">electromagnetic waves</a> (i.e. <a href="/wiki/Light" title="Light">light</a>). This allows standing wave modes to exist with little loss. </p> <div class="mw-heading mw-heading2"><h2 id="Mechanical">Mechanical</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Resonator&action=edit&section=12" title="Edit section: Mechanical"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Mechanical_resonance" title="Mechanical resonance">mechanical resonance</a></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/Mechanical_filter#Resonators" title="Mechanical filter">Mechanical filter § Resonators</a></div> <p>Mechanical resonators are used in <a href="/wiki/Electronic_circuit" title="Electronic circuit">electronic circuits</a> to generate signals of a precise <a href="/wiki/Frequency" title="Frequency">frequency</a>. For example, <a href="/wiki/Crystal_oscillator" title="Crystal oscillator">piezoelectric resonators</a>, commonly made from <a href="/wiki/Quartz_crystal" class="mw-redirect" title="Quartz crystal">quartz</a>, are used as frequency references. Common designs consist of electrodes attached to a piece of quartz, in the shape of a rectangular plate for high frequency applications, or in the shape of a <a href="/wiki/Tuning_fork" title="Tuning fork">tuning fork</a> for low frequency applications. The high dimensional stability and low temperature coefficient of quartz helps keeps resonant frequency constant. In addition, the quartz's <a href="/wiki/Piezoelectricity" title="Piezoelectricity">piezoelectric</a> property converts the mechanical vibrations into an oscillating <a href="/wiki/Voltage" title="Voltage">voltage</a>, which is picked up by the attached electrodes. These <a href="/wiki/Crystal_oscillator" title="Crystal oscillator">crystal oscillators</a> are used in <a href="/wiki/Quartz_clock" title="Quartz clock">quartz clocks</a> and watches, to create the <a href="/wiki/Clock_signal" title="Clock signal">clock signal</a> that runs computers, and to stabilize the output signal from <a href="/wiki/Radio_transmitter" class="mw-redirect" title="Radio transmitter">radio transmitters</a>. </p><p>Mechanical resonators can also be used to induce a standing wave in other media. For example, a multiple degree of freedom system can be created by imposing a base excitation on a cantilever beam. In this case the <a href="/wiki/Standing_wave" title="Standing wave">standing wave</a> is imposed on the beam.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> This type of system can be used as a <a href="/wiki/Sensor" title="Sensor">sensor</a> to track changes in <a href="/wiki/Natural_frequency" title="Natural frequency">frequency</a> or <a href="/wiki/Phase_shift" class="mw-redirect" title="Phase shift">phase</a> of the <a href="/wiki/Resonance" title="Resonance">resonance</a> of the fiber. One application is as a measurement device for <a href="/wiki/Dimensional_metrology" title="Dimensional metrology">dimensional metrology</a>.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Acoustic">Acoustic</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Resonator&action=edit&section=13" title="Edit section: Acoustic"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Acoustic_resonance" title="Acoustic resonance">Acoustic resonance</a></div> <p>The most familiar examples of acoustic resonators are in <a href="/wiki/Musical_instrument" title="Musical instrument">musical instruments</a>. Every musical instrument has resonators. Some generate the sound directly, such as the wooden bars in a <a href="/wiki/Xylophone" title="Xylophone">xylophone</a>, the head of a <a href="/wiki/Drum" title="Drum">drum</a>, the strings in <a href="/wiki/Stringed_instrument" class="mw-redirect" title="Stringed instrument">stringed instruments</a>, and the pipes in an <a href="/wiki/Organ_(instrument)" class="mw-redirect" title="Organ (instrument)">organ</a>. Some modify the sound by enhancing particular frequencies, such as the <a href="/wiki/Sound_box" title="Sound box">sound box</a> of a <a href="/wiki/Guitar" title="Guitar">guitar</a> or <a href="/wiki/Violin" title="Violin">violin</a>. <a href="/wiki/Organ_pipe" title="Organ pipe">Organ pipes</a>, the bodies of <a href="/wiki/Woodwind" class="mw-redirect" title="Woodwind">woodwinds</a>, and the sound boxes of stringed instruments are examples of acoustic cavity resonators. </p> <div class="mw-heading mw-heading3"><h3 id="Automobiles">Automobiles</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Resonator&action=edit&section=14" title="Edit section: Automobiles"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Exhaust_with_Resonator.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Exhaust_with_Resonator.jpg/220px-Exhaust_with_Resonator.jpg" decoding="async" width="220" height="146" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Exhaust_with_Resonator.jpg/330px-Exhaust_with_Resonator.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Exhaust_with_Resonator.jpg/440px-Exhaust_with_Resonator.jpg 2x" data-file-width="4288" data-file-height="2848" /></a><figcaption>A sport motorcycle, equipped with exhaust resonator, designed for performance</figcaption></figure> <p>The exhaust pipes in automobile <a href="/wiki/Exhaust_system" title="Exhaust system">exhaust systems</a> are designed as acoustic resonators that work with the <a href="/wiki/Muffler" title="Muffler">muffler</a> to reduce noise, by making sound waves "cancel each other out".<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> The "exhaust note" is an important feature for some vehicle owners, so both the original manufacturers and the <a href="/wiki/Aftermarket_(automotive)" class="mw-redirect" title="Aftermarket (automotive)">after-market suppliers</a> use the resonator to enhance the sound. In "<a href="/wiki/Tuned_exhaust" title="Tuned exhaust">tuned exhaust</a>" systems designed for performance, the resonance of the exhaust pipes can also be used to remove combustion products from the combustion chamber at a particular engine speed or range of speeds.<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Percussion_instruments">Percussion instruments</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Resonator&action=edit&section=15" title="Edit section: Percussion instruments"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>In many <a href="/wiki/Keyboard_percussion" class="mw-redirect" title="Keyboard percussion">keyboard percussion</a> instruments, below the centre of each note is a tube, which is an <a href="/wiki/Acoustic_resonance" title="Acoustic resonance">acoustic cavity resonator</a>. The length of the tube varies according to the pitch of the note, with higher notes having shorter resonators. The tube is open at the top end and closed at the bottom end, creating a column of air that <a href="/wiki/Resonance" title="Resonance">resonates</a> when the note is struck. This adds depth and volume to the note. In string instruments, the body of the instrument is a resonator. The <a href="/wiki/Tremolo" title="Tremolo">tremolo</a> effect of a <a href="/wiki/Vibraphone" title="Vibraphone">vibraphone</a> is achieved via a mechanism that opens and shuts the resonators. </p> <div class="mw-heading mw-heading3"><h3 id="Stringed_instruments">Stringed instruments</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Resonator&action=edit&section=16" title="Edit section: Stringed instruments"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Steel_guitar-KayEss.1.jpeg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f0/Steel_guitar-KayEss.1.jpeg/170px-Steel_guitar-KayEss.1.jpeg" decoding="async" width="170" height="226" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f0/Steel_guitar-KayEss.1.jpeg/255px-Steel_guitar-KayEss.1.jpeg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f0/Steel_guitar-KayEss.1.jpeg/340px-Steel_guitar-KayEss.1.jpeg 2x" data-file-width="480" data-file-height="637" /></a><figcaption>A <a href="/wiki/Dobro" title="Dobro">Dobro</a>-style <a href="/wiki/Resonator_guitar" title="Resonator guitar">resonator guitar</a></figcaption></figure> <p>String instruments such as the bluegrass <a href="/wiki/Banjo" title="Banjo">banjo</a> may also have resonators. Many five-string banjos have removable resonators, so players can use the instrument with a resonator in <a href="/wiki/Bluegrass_music" title="Bluegrass music">bluegrass</a> style, or without it in <a href="/wiki/Folk_music" title="Folk music">folk music</a> style. The term <i>resonator</i>, used by itself, may also refer to the <a href="/wiki/Resonator_guitar" title="Resonator guitar">resonator guitar</a>. </p><p>The modern <a href="/wiki/Ten-string_guitar" title="Ten-string guitar">ten-string guitar</a>, invented by <a href="/wiki/Narciso_Yepes" title="Narciso Yepes">Narciso Yepes</a>, adds four sympathetic string resonators to the traditional classical guitar. By tuning these resonators in a very specific way (C, B♭, A♭, G♭) and making use of their strongest partials (corresponding to the octaves and fifths of the strings' fundamental tones), the bass strings of the guitar now resonate equally with any of the 12 tones of the chromatic octave. The <a href="/wiki/EBow" title="EBow">guitar resonator</a> is a device for driving guitar string harmonics by an electromagnetic field. This resonance effect is caused by a feedback loop and is applied to drive the fundamental tones, octaves, 5th, 3rd to an infinite <a href="/wiki/Sustain" class="mw-redirect" title="Sustain">sustain</a>. </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Resonator&action=edit&section=17" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Coupling_coefficient_of_resonators" title="Coupling coefficient of resonators">Coupling coefficient of resonators</a></li> <li><a href="/wiki/Crab_cavity" title="Crab cavity">Crab cavity</a></li> <li><a href="/wiki/Nuclear_magnetic_resonance" title="Nuclear magnetic resonance">Nuclear magnetic resonance</a></li> <li><a href="/wiki/Optical_ring_resonators" title="Optical ring resonators">Optical ring resonators</a></li> <li><a href="/wiki/Superconducting_RF" class="mw-redirect" title="Superconducting RF">Superconducting RF</a></li> <li><a href="/wiki/Resonance_chamber" title="Resonance chamber">Resonance chamber</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="References_and_notes">References and notes</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Resonator&action=edit&section=18" title="Edit section: References and notes"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-pozar-1"><span class="mw-cite-backlink">^ <a href="#cite_ref-pozar_1-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-pozar_1-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output 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