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data-unpinned-container-id="vector-main-menu-unpinned-container" > <div class="vector-pinnable-header-label">Huvudmeny</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-main-menu.pin">flytta till sidofältet</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-main-menu.unpin">dölj</button> </div> <div id="p-navigation" class="vector-menu mw-portlet mw-portlet-navigation" > <div class="vector-menu-heading"> Navigering </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-mainpage-description" class="mw-list-item"><a href="/wiki/Portal:Huvudsida" title="Besök huvudsidan [z]" accesskey="z"><span>Huvudsida</span></a></li><li id="n-Introduktion" class="mw-list-item"><a href="/wiki/Wikipedia:Introduktion"><span>Introduktion</span></a></li><li id="n-portal" class="mw-list-item"><a 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href="/wiki/Wikipedia:Hj%C3%A4lp" title="Platsen där du hittar hjälp"><span>Hjälp</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> <a href="/wiki/Portal:Huvudsida" class="mw-logo"> <img class="mw-logo-icon" src="/static/images/icons/wikipedia.png" alt="" aria-hidden="true" height="50" width="50"> <span class="mw-logo-container skin-invert"> <img class="mw-logo-wordmark" alt="Wikipedia" src="/static/images/mobile/copyright/wikipedia-wordmark-en.svg" style="width: 7.5em; height: 1.125em;"> <img class="mw-logo-tagline" alt="" src="/static/images/mobile/copyright/wikipedia-tagline-sv.svg" width="120" height="13" style="width: 7.5em; height: 0.8125em;"> </span> </a> </div> <div class="vector-header-end"> <div id="p-search" role="search" class="vector-search-box-vue vector-search-box-collapses vector-search-box-show-thumbnail vector-search-box-auto-expand-width vector-search-box"> <a href="/wiki/Special:S%C3%B6k" class="cdx-button cdx-button--fake-button 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name="title" value="Special:Sök"> </div> <button class="cdx-button cdx-search-input__end-button">Sök</button> </form> </div> </div> </div> <nav class="vector-user-links vector-user-links-wide" aria-label="Personliga verktyg"> <div class="vector-user-links-main"> <div id="p-vector-user-menu-preferences" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-userpage" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <nav class="vector-appearance-landmark" aria-label="Utseende"> <div id="vector-appearance-dropdown" class="vector-dropdown " title="Ändra utseendet på sidans teckenstorlek, bredd och färg" > <input type="checkbox" id="vector-appearance-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-appearance-dropdown" class="vector-dropdown-checkbox " aria-label="Utseende" > <label id="vector-appearance-dropdown-label" for="vector-appearance-dropdown-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-appearance mw-ui-icon-wikimedia-appearance"></span> <span class="vector-dropdown-label-text">Utseende</span> </label> <div class="vector-dropdown-content"> <div id="vector-appearance-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <div id="p-vector-user-menu-notifications" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-overflow" class="vector-menu mw-portlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="//donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_sv.wikipedia.org&uselang=sv" class=""><span>Stöd Wikipedia</span></a> </li> <li id="pt-createaccount-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Special:Skapa_konto&returnto=Grupphastighet" title="Du uppmuntras att skapa ett konto och logga in, men det är inte obligatoriskt" class=""><span>Skapa konto</span></a> </li> <li id="pt-login-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Special:Inloggning&returnto=Grupphastighet" title="Inloggning ger tillgång till fler funktioner för den som vill skriva och redigera artiklar. [o]" accesskey="o" class=""><span>Logga in</span></a> </li> </ul> </div> </div> </div> <div id="vector-user-links-dropdown" class="vector-dropdown vector-user-menu vector-button-flush-right vector-user-menu-logged-out" title="Fler alternativ" > <input type="checkbox" id="vector-user-links-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-user-links-dropdown" class="vector-dropdown-checkbox " aria-label="Personliga verktyg" > <label id="vector-user-links-dropdown-label" for="vector-user-links-dropdown-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-ellipsis mw-ui-icon-wikimedia-ellipsis"></span> <span class="vector-dropdown-label-text">Personliga verktyg</span> </label> <div class="vector-dropdown-content"> <div id="p-personal" class="vector-menu mw-portlet mw-portlet-personal user-links-collapsible-item" title="Användarmeny" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport" class="user-links-collapsible-item mw-list-item"><a href="//donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_sv.wikipedia.org&uselang=sv"><span>Stöd Wikipedia</span></a></li><li id="pt-createaccount" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Special:Skapa_konto&returnto=Grupphastighet" title="Du uppmuntras att skapa ett konto och logga in, men det är inte obligatoriskt"><span class="vector-icon mw-ui-icon-userAdd mw-ui-icon-wikimedia-userAdd"></span> <span>Skapa konto</span></a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Special:Inloggning&returnto=Grupphastighet" title="Inloggning ger tillgång till fler funktioner för den som vill skriva och redigera artiklar. [o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>Logga in</span></a></li> </ul> </div> </div> <div id="p-user-menu-anon-editor" class="vector-menu mw-portlet mw-portlet-user-menu-anon-editor" > <div class="vector-menu-heading"> Sidor för utloggade redigerare <a href="/wiki/Hj%C3%A4lp:Introduktion" aria-label="Läs mer om redigering"><span>läs mer</span></a> </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-anoncontribs" class="mw-list-item"><a href="/wiki/Special:Mina_bidrag" title="En lista över redigeringar från denna IP-adress [y]" accesskey="y"><span>Bidrag</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/Special:Min_diskussion" title="Diskussion om redigeringar från det här IP-numret [n]" accesskey="n"><span>Diskussion</span></a></li> </ul> </div> </div> </div> </div> </nav> </div> </header> </div> <div class="mw-page-container"> <div class="mw-page-container-inner"> <div class="vector-sitenotice-container"> <div id="siteNotice"></div> </div> <div class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="Webbplats"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="Innehåll" data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">Innehåll</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">flytta till sidofältet</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">dölj</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">Inledning</div> </a> </li> <li id="toc-Beroendet_på_dispersion" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Beroendet_på_dispersion"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Beroendet på dispersion</span> </div> </a> <ul id="toc-Beroendet_på_dispersion-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="Innehåll" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Växla innehållsförteckningen" > <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">Växla innehållsförteckningen</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">Grupphastighet</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="Gå till en artikel på ett annat språk. Tillgänglig på 31 språk" > <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-31" 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">31 språk</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%B3%D8%B1%D8%B9%D8%A9_%D8%A7%D9%84%D8%B2%D9%85%D8%B1%D8%A9" title="سرعة الزمرة – arabiska" lang="ar" hreflang="ar" data-title="سرعة الزمرة" data-language-autonym="العربية" data-language-local-name="arabiska" 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%93%D1%80%D1%83%D0%BF%D0%B0%D0%B2%D0%B0%D1%8F_%D1%81%D0%BA%D0%BE%D1%80%D0%B0%D1%81%D1%86%D1%8C" title="Групавая скорасць – belarusiska" lang="be" hreflang="be" data-title="Групавая скорасць" data-language-autonym="Беларуская" data-language-local-name="belarusiska" 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/Velocitat_de_grup" title="Velocitat de grup – katalanska" lang="ca" hreflang="ca" data-title="Velocitat de grup" data-language-autonym="Català" data-language-local-name="katalanska" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Grupov%C3%A1_rychlost" title="Grupová rychlost – tjeckiska" lang="cs" hreflang="cs" data-title="Grupová rychlost" data-language-autonym="Čeština" data-language-local-name="tjeckiska" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Gruppengeschwindigkeit" title="Gruppengeschwindigkeit – tyska" lang="de" hreflang="de" data-title="Gruppengeschwindigkeit" data-language-autonym="Deutsch" data-language-local-name="tyska" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Group_velocity" title="Group velocity – engelska" lang="en" hreflang="en" data-title="Group velocity" data-language-autonym="English" data-language-local-name="engelska" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Velocidad_de_grupo" title="Velocidad de grupo – spanska" lang="es" hreflang="es" data-title="Velocidad de grupo" data-language-autonym="Español" data-language-local-name="spanska" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Grupa_rapido" title="Grupa rapido – esperanto" lang="eo" hreflang="eo" data-title="Grupa rapido" data-language-autonym="Esperanto" data-language-local-name="esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%B3%D8%B1%D8%B9%D8%AA_%DA%AF%D8%B1%D9%88%D9%87" title="سرعت گروه – persiska" lang="fa" hreflang="fa" data-title="سرعت گروه" data-language-autonym="فارسی" data-language-local-name="persiska" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Vitesse_d%27une_onde#Vitesse_de_groupe" title="Vitesse d'une onde – franska" lang="fr" hreflang="fr" data-title="Vitesse d'une onde" data-language-autonym="Français" data-language-local-name="franska" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EA%B5%B0%EC%86%8D%EB%8F%84" title="군속도 – koreanska" lang="ko" hreflang="ko" data-title="군속도" data-language-autonym="한국어" data-language-local-name="koreanska" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D4%BD%D5%B4%D5%A2%D5%A1%D5%B5%D5%AB%D5%B6_%D5%A1%D6%80%D5%A1%D5%A3%D5%B8%D6%82%D5%A9%D5%B5%D5%B8%D6%82%D5%B6" title="Խմբային արագություն – armeniska" lang="hy" hreflang="hy" data-title="Խմբային արագություն" data-language-autonym="Հայերեն" data-language-local-name="armeniska" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Velocit%C3%A0_di_gruppo" title="Velocità di gruppo – italienska" lang="it" hreflang="it" data-title="Velocità di gruppo" data-language-autonym="Italiano" data-language-local-name="italienska" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%9E%D7%94%D7%99%D7%A8%D7%95%D7%AA_%D7%97%D7%91%D7%95%D7%A8%D7%94" title="מהירות חבורה – hebreiska" lang="he" hreflang="he" data-title="מהירות חבורה" data-language-autonym="עברית" data-language-local-name="hebreiska" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%AF%E1%83%92%E1%83%A3%E1%83%A4%E1%83%A3%E1%83%A0%E1%83%98_%E1%83%A1%E1%83%98%E1%83%A9%E1%83%A5%E1%83%90%E1%83%A0%E1%83%94" title="ჯგუფური სიჩქარე – georgiska" lang="ka" hreflang="ka" data-title="ჯგუფური სიჩქარე" data-language-autonym="ქართული" data-language-local-name="georgiska" 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%A2%D0%BE%D0%BF%D1%82%D1%8B%D2%9B_%D0%B6%D1%8B%D0%BB%D0%B4%D0%B0%D0%BC%D0%B4%D1%8B%D2%9B" title="Топтық жылдамдық – kazakiska" lang="kk" hreflang="kk" data-title="Топтық жылдамдық" data-language-autonym="Қазақша" data-language-local-name="kazakiska" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Grupinis_greitis" title="Grupinis greitis – litauiska" lang="lt" hreflang="lt" data-title="Grupinis greitis" data-language-autonym="Lietuvių" data-language-local-name="litauiska" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%93%D1%80%D1%83%D0%BF%D0%BD%D0%B0_%D0%B1%D1%80%D0%B7%D0%B8%D0%BD%D0%B0" title="Групна брзина – makedonska" lang="mk" hreflang="mk" data-title="Групна брзина" data-language-autonym="Македонски" data-language-local-name="makedonska" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Voortplantingssnelheid#Fase-_en_groepssnelheid" title="Voortplantingssnelheid – nederländska" lang="nl" hreflang="nl" data-title="Voortplantingssnelheid" data-language-autonym="Nederlands" data-language-local-name="nederländska" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E7%BE%A4%E9%80%9F%E5%BA%A6" title="群速度 – japanska" lang="ja" hreflang="ja" data-title="群速度" data-language-autonym="日本語" data-language-local-name="japanska" 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/Gruppefart" title="Gruppefart – norskt bokmål" lang="nb" hreflang="nb" data-title="Gruppefart" data-language-autonym="Norsk bokmål" data-language-local-name="norskt 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/Gruppefart" title="Gruppefart – nynorska" lang="nn" hreflang="nn" data-title="Gruppefart" data-language-autonym="Norsk nynorsk" data-language-local-name="nynorska" 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/Pr%C4%99dko%C5%9B%C4%87_grupowa" title="Prędkość grupowa – polska" lang="pl" hreflang="pl" data-title="Prędkość grupowa" data-language-autonym="Polski" data-language-local-name="polska" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%93%D1%80%D1%83%D0%BF%D0%BF%D0%BE%D0%B2%D0%B0%D1%8F_%D1%81%D0%BA%D0%BE%D1%80%D0%BE%D1%81%D1%82%D1%8C" title="Групповая скорость – ryska" lang="ru" hreflang="ru" data-title="Групповая скорость" data-language-autonym="Русский" data-language-local-name="ryska" 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/Group_velocity" title="Group velocity – Simple English" lang="en-simple" hreflang="en-simple" data-title="Group velocity" 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-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Skupinska_hitrost" title="Skupinska hitrost – slovenska" lang="sl" hreflang="sl" data-title="Skupinska hitrost" data-language-autonym="Slovenščina" data-language-local-name="slovenska" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Ryhm%C3%A4nopeus" title="Ryhmänopeus – finska" lang="fi" hreflang="fi" data-title="Ryhmänopeus" data-language-autonym="Suomi" data-language-local-name="finska" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Grup_h%C4%B1z%C4%B1" title="Grup hızı – turkiska" lang="tr" hreflang="tr" data-title="Grup hızı" data-language-autonym="Türkçe" data-language-local-name="turkiska" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%93%D1%80%D1%83%D0%BF%D0%BE%D0%B2%D0%B0_%D1%88%D0%B2%D0%B8%D0%B4%D0%BA%D1%96%D1%81%D1%82%D1%8C" title="Групова швидкість – ukrainska" lang="uk" hreflang="uk" data-title="Групова швидкість" data-language-autonym="Українська" data-language-local-name="ukrainska" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/V%E1%BA%ADn_t%E1%BB%91c_nh%C3%B3m" title="Vận tốc nhóm – vietnamesiska" lang="vi" hreflang="vi" data-title="Vận tốc nhóm" data-language-autonym="Tiếng Việt" data-language-local-name="vietnamesiska" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E7%BE%A4%E9%80%9F%E5%BA%A6" title="群速度 – kinesiska" lang="zh" hreflang="zh" data-title="群速度" data-language-autonym="中文" data-language-local-name="kinesiska" class="interlanguage-link-target"><span>中文</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/Q217361#sitelinks-wikipedia" title="Redigera interwikilänkar" class="wbc-editpage">Redigera länkar</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="Namnrymder"> <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/Grupphastighet" title="Visa innehållssidan [c]" accesskey="c"><span>Artikel</span></a></li><li id="ca-talk" class="new vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Diskussion:Grupphastighet&action=edit&redlink=1" 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id="right-navigation" class="vector-collapsible"> <nav aria-label="Visningar"> <div id="p-views" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-views" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-view" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Grupphastighet"><span>Läs</span></a></li><li id="ca-ve-edit" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Grupphastighet&veaction=edit" title="Redigera denna sida [v]" accesskey="v"><span>Redigera</span></a></li><li id="ca-edit" class="collapsible vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Grupphastighet&action=edit" title="Redigera wikitexten för den här sidan [e]" accesskey="e"><span>Redigera wikitext</span></a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Grupphastighet&action=history" title="Tidigare versioner av sidan [h]" accesskey="h"><span>Visa historik</span></a></li> </ul> </div> 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href="/wiki/Fil:Wave_group.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/bd/Wave_group.gif/380px-Wave_group.gif" decoding="async" width="380" height="29" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/b/bd/Wave_group.gif 1.5x" data-file-width="465" data-file-height="36" /></a><figcaption>Olika hastigheter av två vågor och deras <a href="/wiki/Sv%C3%A4vning" title="Svävning">svävningsmönster</a>; den gröna pricken anger grupphastigheten, som modulationerna utbreder sig med; den röda pricken löper med <a href="/wiki/V%C3%A5ghastighet" title="Våghastighet">vågornas fashastighet</a>.</figcaption></figure> <p><b>Grupphastighet</b> är den hastighet som <a href="/wiki/Modulation" title="Modulation">modulationer</a> av en <a href="/wiki/V%C3%A5gr%C3%B6relse" title="Vågrörelse">vågrörelse</a> utbreder sig med. När <a href="/wiki/V%C3%A5ghastighet" title="Våghastighet">våghastigheten</a> är oberoende av frekvens, är grupphastigheten lika med vågens utbredningshastighet och med fashastighet. Detta är fallet för <a href="/wiki/Ljusets_hastighet_i_vakuum" class="mw-redirect" title="Ljusets hastighet i vakuum">ljusets hastighet i vakuum</a> och vid god approximation även för <a href="/wiki/Ljudhastighet" title="Ljudhastighet">hastigheten av ljud</a>. Men när vågen färdas i ett medium med <a href="/wiki/Dispersion" title="Dispersion">dispersion</a>, kan grupphastigheten båda ha större och lägre värden. Grupphastighet kan i många fall likställas med <a href="/w/index.php?title=Signalhastighet&action=edit&redlink=1" class="new" title="Signalhastighet [inte skriven än]">signalhastighet</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Beroendet_på_dispersion"><span id="Beroendet_p.C3.A5_dispersion"></span>Beroendet på dispersion</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Grupphastighet&veaction=edit&section=1" title="Redigera avsnitt: Beroendet på dispersion" class="mw-editsection-visualeditor"><span>redigera</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Grupphastighet&action=edit&section=1" title="Redigera avsnitts källkod: Beroendet på dispersion"><span>redigera wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Matematiskt kan man beskriva en fortskridande våg i en dimension med uttrycket </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 y(x,t)=A\sin \left({\frac {2\pi x}{\lambda }}-{\frac {2\pi t}{\tau }}+\phi \right)=Ae^{i(kx-\omega t+\phi )},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>y</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo>,</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>A</mi> <mi>sin</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>2</mn> <mi>π</mi> <mi>x</mi> </mrow> <mi>λ</mi> </mfrac> </mrow> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>2</mn> <mi>π</mi> <mi>t</mi> </mrow> <mi>τ</mi> </mfrac> </mrow> <mo>+</mo> <mi>ϕ</mi> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mi>A</mi> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo stretchy="false">(</mo> <mi>k</mi> <mi>x</mi> <mo>−</mo> <mi>ω</mi> <mi>t</mi> <mo>+</mo> <mi>ϕ</mi> <mo stretchy="false">)</mo> </mrow> </msup> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle y(x,t)=A\sin \left({\frac {2\pi x}{\lambda }}-{\frac {2\pi t}{\tau }}+\phi \right)=Ae^{i(kx-\omega t+\phi )},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e1860aa6a4155351314aa88474c94841308dea6f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:49.171ex; height:6.176ex;" alt="{\displaystyle y(x,t)=A\sin \left({\frac {2\pi x}{\lambda }}-{\frac {2\pi t}{\tau }}+\phi \right)=Ae^{i(kx-\omega t+\phi )},}"></span></dd></dl> <p>där <i>k</i>=2π/λ är det <a href="/wiki/Cirkul%C3%A4ra_v%C3%A5gtalet" class="mw-redirect" title="Cirkulära vågtalet">cirkulära vågtalet</a> och ω=2πf är <a href="/wiki/Vinkelfrekvens" class="mw-redirect" title="Vinkelfrekvens">vinkelfrekvensen</a>. En punkt med konstant fasfaktor <i>kx-ωt+φ</i> löper med en hastighet </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_{\mathrm {fas} }={\frac {\omega }{k}}=f\cdot \lambda .}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">f</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">s</mi> </mrow> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>ω</mi> <mi>k</mi> </mfrac> </mrow> <mo>=</mo> <mi>f</mi> <mo>⋅</mo> <mi>λ</mi> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v_{\mathrm {fas} }={\frac {\omega }{k}}=f\cdot \lambda .}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bd1e4dd1cb635146139e68c0b1ff435192a44577" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:16.88ex; height:4.843ex;" alt="{\displaystyle v_{\mathrm {fas} }={\frac {\omega }{k}}=f\cdot \lambda .}"></span></dd></dl> <p><b>Grupphastighet</b>en är dock </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_{\mathrm {grupp} }={\frac {\mathrm {d} \omega }{\mathrm {d} k}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">g</mi> <mi mathvariant="normal">r</mi> <mi mathvariant="normal">u</mi> <mi mathvariant="normal">p</mi> <mi mathvariant="normal">p</mi> </mrow> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>ω</mi> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>k</mi> </mrow> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v_{\mathrm {grupp} }={\frac {\mathrm {d} \omega }{\mathrm {d} k}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c2d86fb7b147bf09d8c2a9b7f5c49c58659d9a87" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:12.888ex; height:5.509ex;" alt="{\displaystyle v_{\mathrm {grupp} }={\frac {\mathrm {d} \omega }{\mathrm {d} k}}.}"></span></dd></dl> <p>Detta kan man härleda genom att betrakta utbredningshastighet av två vågor med frekvenser ω<sub>1</sub>, ω<sub>2</sub> och vågtalen <i>k</i><sub>1</sub>, <i>k</i><sub>2</sub>. Summan kan skrivas som medelfrekvensen modulerad med en amplitudfaktor <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 \sin((k_{1}-k_{2})x-(\omega _{1}-\omega _{2})t)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mo stretchy="false">(</mo> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>−</mo> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">)</mo> <mi>x</mi> <mo>−</mo> <mo stretchy="false">(</mo> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>−</mo> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">)</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sin((k_{1}-k_{2})x-(\omega _{1}-\omega _{2})t)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3dd6161e565358fc64ed370b09084f2f951ee7a8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:28.505ex; height:2.843ex;" alt="{\displaystyle \sin((k_{1}-k_{2})x-(\omega _{1}-\omega _{2})t)}"></span>. <a href="/wiki/Sv%C3%A4vning" title="Svävning">Svävningarna</a> utbreder sig därför med <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 (\omega _{1}-\omega _{2})/(k_{1}-k_{2})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>−</mo> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mo stretchy="false">(</mo> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>−</mo> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (\omega _{1}-\omega _{2})/(k_{1}-k_{2})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5be7bb5eff6be1a7d9c8df96d2d44287302317be" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:19.993ex; height:2.843ex;" alt="{\displaystyle (\omega _{1}-\omega _{2})/(k_{1}-k_{2})}"></span>. Vid <a href="/wiki/Infinitesimal" title="Infinitesimal">infinitesimala</a> skillnader i frekvens ger det resultatet ovan. </p><p>Sambandet mellan frekvens och <a href="/wiki/V%C3%A5gl%C3%A4ngd" title="Våglängd">våglängd</a> kan ges med en funktion ω(<i>k</i>), en dispersionsrelation. I många fall är det dock hastigheten (fashastigheten) som ges som funktion av våglängd. Om man skriver <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v_{\rm {fas}}k=\omega }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">f</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">s</mi> </mrow> </mrow> </msub> <mi>k</mi> <mo>=</mo> <mi>ω</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v_{\rm {fas}}k=\omega }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1281e013305bfc17c3b1ba48324f465dc8b523d5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:9.197ex; height:2.509ex;" alt="{\displaystyle v_{\rm {fas}}k=\omega }"></span> in i definitionen för grupphastighet, får man </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_{\mathrm {g} }=v_{\mathrm {fas} }+k{\frac {\mathrm {d} v_{\mathrm {fas} }}{\mathrm {d} k}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">g</mi> </mrow> </mrow> </msub> <mo>=</mo> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">f</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">s</mi> </mrow> </mrow> </msub> <mo>+</mo> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">f</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">s</mi> </mrow> </mrow> </msub> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>k</mi> </mrow> </mfrac> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v_{\mathrm {g} }=v_{\mathrm {fas} }+k{\frac {\mathrm {d} v_{\mathrm {fas} }}{\mathrm {d} k}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/435bb8c3dde3499972b7d6415b7dbeffd31e3f8a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:18.99ex; height:5.509ex;" alt="{\displaystyle v_{\mathrm {g} }=v_{\mathrm {fas} }+k{\frac {\mathrm {d} v_{\mathrm {fas} }}{\mathrm {d} k}},}"></span></dd></dl> <p>som enkelt kan skrivas i termer av våglängd <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 =2\pi /k}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>λ</mi> <mo>=</mo> <mn>2</mn> <mi>π</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mi>k</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lambda =2\pi /k}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/baa6792aa5b5f588516826c964be9d70b98591b3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.322ex; height:2.843ex;" alt="{\displaystyle \lambda =2\pi /k}"></span> som </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_{\mathrm {g} }=v_{\mathrm {fas} }-\lambda {\frac {\mathrm {d} v_{\mathrm {fas} }}{\mathrm {d} \lambda }}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">g</mi> </mrow> </mrow> </msub> <mo>=</mo> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">f</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">s</mi> </mrow> </mrow> </msub> <mo>−</mo> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">f</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">s</mi> </mrow> </mrow> </msub> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>λ</mi> </mrow> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v_{\mathrm {g} }=v_{\mathrm {fas} }-\lambda {\frac {\mathrm {d} v_{\mathrm {fas} }}{\mathrm {d} \lambda }}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/177829cdef6595ec3603938d036df58a9be727f0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:19.134ex; height:5.509ex;" alt="{\displaystyle v_{\mathrm {g} }=v_{\mathrm {fas} }-\lambda {\frac {\mathrm {d} v_{\mathrm {fas} }}{\mathrm {d} \lambda }}.}"></span></dd></dl>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Hämtad från ”<a dir="ltr" href="https://sv.wikipedia.org/w/index.php?title=Grupphastighet&oldid=50538958">https://sv.wikipedia.org/w/index.php?title=Grupphastighet&oldid=50538958</a>”</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Wikipedia:Kategorier" title="Wikipedia:Kategorier">Kategori</a>: <ul><li><a href="/wiki/Kategori:V%C3%A5gor" title="Kategori:Vågor">Vågor</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> Sidan redigerades senast den 30 maj 2022 kl. 19.38.</li> <li id="footer-info-copyright">Wikipedias text är tillgänglig under licensen <a rel="nofollow" class="external text" href="//creativecommons.org/licenses/by-sa/4.0/deed.sv">Creative Commons Erkännande-dela-lika 4.0 Unported</a>. 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