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Svävning – Wikipedia

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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 href="/wiki/Wikipedia:Deltagarportalen" title="Om projektet, vad du kan göra, var man kan hitta saker"><span>Deltagarportalen</span></a></li><li id="n-Bybrunnen" class="mw-list-item"><a href="/wiki/Wikipedia:Bybrunnen"><span>Bybrunnen</span></a></li><li id="n-recentchanges" class="mw-list-item"><a href="/wiki/Special:Senaste_%C3%A4ndringar" title="Lista över de senaste ändringarna på wikin [r]" accesskey="r"><span>Senaste ändringarna</span></a></li><li id="n-randompage" class="mw-list-item"><a href="/wiki/Special:Slumpsida" title="Gå till en slumpmässigt vald sida [x]" accesskey="x"><span>Slumpartikel</span></a></li><li id="n-filuppladdning" class="mw-list-item"><a href="//commons.wikimedia.org/wiki/Special:UploadWizard" title="Ladda upp filer till Wikimedia Commons"><span>Ladda upp filer</span></a></li><li id="n-Kontakta-Wikipedia" class="mw-list-item"><a href="/wiki/Wikipedia:Kontakt"><span>Kontakta Wikipedia</span></a></li><li id="n-help" class="mw-list-item"><a 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"> 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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&amp;utm_medium=sidebar&amp;utm_campaign=C13_sv.wikipedia.org&amp;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&amp;returnto=Sv%C3%A4vning" 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&amp;returnto=Sv%C3%A4vning" 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&amp;utm_medium=sidebar&amp;utm_campaign=C13_sv.wikipedia.org&amp;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&amp;returnto=Sv%C3%A4vning" 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&amp;returnto=Sv%C3%A4vning" 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"><!-- CentralNotice --></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-Matematisk_förklaring" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Matematisk_förklaring"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Matematisk förklaring</span> </div> </a> <ul id="toc-Matematisk_förklaring-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Är_svävning_modulation?" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Är_svävning_modulation?"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Är svävning modulation?</span> </div> </a> <ul id="toc-Är_svävning_modulation?-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Se_även" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Se_även"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Se även</span> </div> </a> <ul id="toc-Se_även-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Externa_länkar" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Externa_länkar"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Externa länkar</span> </div> </a> <ul id="toc-Externa_länkar-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">Svävning</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 28 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-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 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/%D9%86%D8%A8%D8%B6%D8%A9_(%D8%B5%D9%88%D8%AA)" title="نبضة (صوت) – arabiska" lang="ar" hreflang="ar" data-title="نبضة (صوت)" data-language-autonym="العربية" data-language-local-name="arabiska" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%91%D0%B8%D0%B5%D0%BD%D0%B5_(%D1%84%D0%B8%D0%B7%D0%B8%D0%BA%D0%B0)" title="Биене (физика) – bulgariska" lang="bg" hreflang="bg" data-title="Биене (физика)" data-language-autonym="Български" data-language-local-name="bulgariska" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%A2%D0%B0%D0%BF%C4%83_(%D1%84%D0%B8%D0%B7%D0%B8%D0%BA%D0%B0)" title="Тапă (физика) – tjuvasjiska" lang="cv" hreflang="cv" data-title="Тапă (физика)" data-language-autonym="Чӑвашла" data-language-local-name="tjuvasjiska" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Z%C3%A1zn%C4%9Bj" title="Zázněj – tjeckiska" lang="cs" hreflang="cs" data-title="Zázněj" 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/Schwebung" title="Schwebung – tyska" lang="de" hreflang="de" data-title="Schwebung" data-language-autonym="Deutsch" data-language-local-name="tyska" 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/Tuiklemine" title="Tuiklemine – estniska" lang="et" hreflang="et" data-title="Tuiklemine" data-language-autonym="Eesti" data-language-local-name="estniska" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Beat_(acoustics)" title="Beat (acoustics) – engelska" lang="en" hreflang="en" data-title="Beat (acoustics)" 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/Batimiento" title="Batimiento – spanska" lang="es" hreflang="es" data-title="Batimiento" data-language-autonym="Español" data-language-local-name="spanska" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Battement_(acoustique)" title="Battement (acoustique) – franska" lang="fr" hreflang="fr" data-title="Battement (acoustique)" data-language-autonym="Français" data-language-local-name="franska" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/B%C3%A9imeanna" title="Béimeanna – iriska" lang="ga" hreflang="ga" data-title="Béimeanna" data-language-autonym="Gaeilge" data-language-local-name="iriska" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%B5%E0%A4%BF%E0%A4%B8%E0%A5%8D%E0%A4%AA%E0%A4%A8%E0%A5%8D%E0%A4%A6" title="विस्पन्द – hindi" lang="hi" hreflang="hi" data-title="विस्पन्द" 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/Battimenti_(musica)" title="Battimenti (musica) – italienska" lang="it" hreflang="it" data-title="Battimenti (musica)" 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%A4%D7%A2%D7%99%D7%9E%D7%94_(%D7%90%D7%A7%D7%95%D7%A1%D7%98%D7%99%D7%A7%D7%94)" title="פעימה (אקוסטיקה) – hebreiska" lang="he" hreflang="he" data-title="פעימה (אקוסטיקה)" data-language-autonym="עברית" data-language-local-name="hebreiska" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/Kadans" title="Kadans – haitiska" lang="ht" hreflang="ht" data-title="Kadans" data-language-autonym="Kreyòl ayisyen" data-language-local-name="haitiska" class="interlanguage-link-target"><span>Kreyòl ayisyen</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Lebeg%C3%A9s_(hangtan)" title="Lebegés (hangtan) – ungerska" lang="hu" hreflang="hu" data-title="Lebegés (hangtan)" data-language-autonym="Magyar" data-language-local-name="ungerska" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%AC%E0%B5%80%E0%B4%B1%E0%B5%8D%E0%B4%B1%E0%B5%8D" title="ബീറ്റ് – malayalam" lang="ml" hreflang="ml" data-title="ബീറ്റ്" data-language-autonym="മലയാളം" data-language-local-name="malayalam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Zweving" title="Zweving – nederländska" lang="nl" hreflang="nl" data-title="Zweving" 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/%E3%81%86%E3%81%AA%E3%82%8A" title="うなり – japanska" lang="ja" hreflang="ja" data-title="うなり" 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/Svevning" title="Svevning – norskt bokmål" lang="nb" hreflang="nb" data-title="Svevning" 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/Svevning" title="Svevning – nynorska" lang="nn" hreflang="nn" data-title="Svevning" 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/Dudnienie" title="Dudnienie – polska" lang="pl" hreflang="pl" data-title="Dudnienie" data-language-autonym="Polski" data-language-local-name="polska" 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/Batimentos" title="Batimentos – portugisiska" lang="pt" hreflang="pt" data-title="Batimentos" data-language-autonym="Português" data-language-local-name="portugisiska" 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%91%D0%B8%D0%B5%D0%BD%D0%B8%D1%8F" title="Биения – ryska" lang="ru" hreflang="ru" data-title="Биения" data-language-autonym="Русский" data-language-local-name="ryska" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Huojunta" title="Huojunta – finska" lang="fi" hreflang="fi" data-title="Huojunta" data-language-autonym="Suomi" data-language-local-name="finska" 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%B5%E0%AE%BF%E0%AE%AE%E0%AF%8D%E0%AE%AE%E0%AE%B2%E0%AF%8D_(%E0%AE%92%E0%AE%B2%E0%AE%BF%E0%AE%AF%E0%AE%BF%E0%AE%AF%E0%AE%B2%E0%AF%8D)" title="விம்மல் (ஒலியியல்) – tamil" lang="ta" hreflang="ta" data-title="விம்மல் (ஒலியியல்)" 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%91%D0%B8%D1%82%D1%82%D1%8F" title="Биття – ukrainska" lang="uk" hreflang="uk" data-title="Биття" 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/Hi%E1%BB%87n_t%C6%B0%E1%BB%A3ng_ph%C3%A1ch" title="Hiện tượng phách – vietnamesiska" lang="vi" hreflang="vi" data-title="Hiện tượng phách" 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/%E6%8B%8D%E9%A2%91" title="拍频 – kinesiska" lang="zh" hreflang="zh" data-title="拍频" 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/Q829522#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/Sv%C3%A4vning" title="Visa innehållssidan [c]" accesskey="c"><span>Artikel</span></a></li><li id="ca-talk" class="vector-tab-noicon mw-list-item"><a href="/wiki/Diskussion:Sv%C3%A4vning" rel="discussion" title="Diskussion om innehållssidan [t]" accesskey="t"><span>Diskussion</span></a></li> </ul> </div> </div> <div id="vector-variants-dropdown" class="vector-dropdown emptyPortlet" > <input type="checkbox" id="vector-variants-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-variants-dropdown" class="vector-dropdown-checkbox " aria-label="Ändra språkvariant" > <label id="vector-variants-dropdown-label" for="vector-variants-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">svenska</span> </label> <div class="vector-dropdown-content"> <div id="p-variants" class="vector-menu mw-portlet mw-portlet-variants emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> </div> </div> </nav> </div> <div 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/Sv%C3%A4vning"><span>Läs</span></a></li><li id="ca-ve-edit" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Sv%C3%A4vning&amp;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=Sv%C3%A4vning&amp;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=Sv%C3%A4vning&amp;action=history" title="Tidigare versioner av sidan [h]" accesskey="h"><span>Visa historik</span></a></li> </ul> </div> </div> </nav> <nav class="vector-page-tools-landmark" aria-label="Sidverktyg"> <div id="vector-page-tools-dropdown" class="vector-dropdown vector-page-tools-dropdown" > <input type="checkbox" id="vector-page-tools-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-tools-dropdown" class="vector-dropdown-checkbox " aria-label="Verktyg" > <label id="vector-page-tools-dropdown-label" for="vector-page-tools-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">Verktyg</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-tools-unpinned-container" class="vector-unpinned-container"> <div id="vector-page-tools" class="vector-page-tools vector-pinnable-element"> <div class="vector-pinnable-header vector-page-tools-pinnable-header vector-pinnable-header-unpinned" data-feature-name="page-tools-pinned" data-pinnable-element-id="vector-page-tools" data-pinned-container-id="vector-page-tools-pinned-container" data-unpinned-container-id="vector-page-tools-unpinned-container" > <div class="vector-pinnable-header-label">Verktyg</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">flytta till sidofältet</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">dölj</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="Fler alternativ" > <div class="vector-menu-heading"> Åtgärder </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-more-view" class="selected vector-more-collapsible-item mw-list-item"><a href="/wiki/Sv%C3%A4vning"><span>Läs</span></a></li><li id="ca-more-ve-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Sv%C3%A4vning&amp;veaction=edit" title="Redigera denna sida [v]" accesskey="v"><span>Redigera</span></a></li><li id="ca-more-edit" class="collapsible vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Sv%C3%A4vning&amp;action=edit" title="Redigera wikitexten för den här sidan [e]" accesskey="e"><span>Redigera wikitext</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Sv%C3%A4vning&amp;action=history"><span>Visa historik</span></a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" > <div class="vector-menu-heading"> Allmänt </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/Special:L%C3%A4nkar_hit/Sv%C3%A4vning" title="Lista över alla wikisidor som länkar hit [j]" accesskey="j"><span>Sidor som länkar hit</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/Special:Senaste_relaterade_%C3%A4ndringar/Sv%C3%A4vning" rel="nofollow" title="Visa senaste ändringarna av sidor som den här sidan länkar till [k]" accesskey="k"><span>Relaterade ändringar</span></a></li><li id="t-specialpages" class="mw-list-item"><a href="/wiki/Special:Specialsidor" title="Lista över alla specialsidor [q]" accesskey="q"><span>Specialsidor</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=Sv%C3%A4vning&amp;oldid=55176324" title="Permanent länk till den här versionen av sidan"><span>Permanent 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mw-list-item"><a href="https://commons.wikimedia.org/wiki/Category:Beat_frequencies" hreflang="en"><span>Commons</span></a></li><li id="t-wikibase" class="wb-otherproject-link wb-otherproject-wikibase-dataitem mw-list-item"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q829522" title="Länk till anslutet databasobjekt [g]" accesskey="g"><span>Wikidata-objekt</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> </div> </div> </div> <div class="vector-column-end"> <div class="vector-sticky-pinned-container"> <nav class="vector-page-tools-landmark" aria-label="Sidverktyg"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Utseende"> <div id="vector-appearance-pinned-container" class="vector-pinned-container"> <div id="vector-appearance" class="vector-appearance vector-pinnable-element"> <div class="vector-pinnable-header vector-appearance-pinnable-header 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id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="sv" dir="ltr"><figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Fil:Beating_Frequency.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/2e/Beating_Frequency.svg/250px-Beating_Frequency.svg.png" decoding="async" width="250" height="126" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/2e/Beating_Frequency.svg/375px-Beating_Frequency.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/2e/Beating_Frequency.svg/500px-Beating_Frequency.svg.png 2x" data-file-width="1160" data-file-height="586" /></a><figcaption>En ton som pulserar med svävningsperiod 1/<i>f</i><sub>s</sub> kan skrivas som produkt av två sinusvågor med mycket olika frekvens (som ovan), eller som summa av två toner med nästan samma frekvens.</figcaption></figure> <p><b>Svävning</b> är ett <a href="/wiki/Ljud" title="Ljud">ljudfenomen</a> som uppstår då två ungefär lika starka <a href="/wiki/Ton_(ljud)" class="mw-redirect" title="Ton (ljud)">toner</a> som ligger mycket nära varandra i <a href="/wiki/Frekvens" title="Frekvens">frekvens</a> når <a href="/wiki/%C3%96rat" class="mw-redirect" title="Örat">örat</a> samtidigt. Ljudet uppfattas som en enda ton som regelbundet ökar och minskar i styrka. Det är denna styrkevariation som kallas för svävning. Ju mindre frekvensskillnad mellan tonerna, desto långsammare blir svävningen. </p><p>En musiker som <a href="/wiki/St%C3%A4mning_(musik)" title="Stämning (musik)">stämmer</a> sitt <a href="/wiki/Musikinstrument" title="Musikinstrument">instrument</a> efter en stämton, lyssnar efter svävningen och justerar instrumentet tills svävningen upphör. Då ljuder instrumentet med samma frekvens som stämtonen. </p><p>Beräkningsmässigt är det alltid likvärdigt att beskriva två toner var för sig eller att uttrycka dem som en enda ton med en frekvens mitt emellan ursprungstonerna och som svävar med en frekvens som är skillnaden mellan ursprungstonernas frekvenser. Det gäller oavsett hur mycket tonerna skiljer i tonhöjd. Örat uppfattar dock normalt två toner var för sig. Det är bara när tonerna ligger så nära varandra i tonhöjd att örat har svårt att skilja dem åt, som vi övergår till att uppfatta dem som en svävning. </p><p><a href="/wiki/Fysik" title="Fysik">Fysikaliskt</a> kan man förklara en svävning som två <a href="/wiki/V%C3%A5gr%C3%B6relse" title="Vågrörelse">vågor</a> som först samarbetar, men som efter ett tag kommer ur fas därför att den ena vågen släpar efter (har något lägre frekvens). Så småningom motarbetar de varandra helt och ljudstyrkan når ett minimum. Efter ytterligare eftersläpning kommer svängningarna alltmer i takt och ljudstyrkan ökar. Man säger också att vågorna <a href="/wiki/Interferens_(v%C3%A5gr%C3%B6relse)" title="Interferens (vågrörelse)">interfererar</a>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Matematisk_förklaring"><span id="Matematisk_f.C3.B6rklaring"></span>Matematisk förklaring</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Sv%C3%A4vning&amp;veaction=edit&amp;section=1" title="Redigera avsnitt: Matematisk förklaring" class="mw-editsection-visualeditor"><span>redigera</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Sv%C3%A4vning&amp;action=edit&amp;section=1" title="Redigera avsnitts källkod: Matematisk förklaring"><span>redigera wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Ur de grundläggande trigonometriska sambanden för addition och subtraktion av två vinklar <i>a</i> och <i>b</i> får vi </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 \sin(a+b)+\sin(a-b)=2\sin(a)\cos(b)\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>sin</mi> <mo>&#x2061;<!-- ⁡ --></mo> <mo stretchy="false">(</mo> <mi>a</mi> <mo>+</mo> <mi>b</mi> <mo stretchy="false">)</mo> <mo>+</mo> <mi>sin</mi> <mo>&#x2061;<!-- ⁡ --></mo> <mo stretchy="false">(</mo> <mi>a</mi> <mo>&#x2212;<!-- − --></mo> <mi>b</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mn>2</mn> <mi>sin</mi> <mo>&#x2061;<!-- ⁡ --></mo> <mo stretchy="false">(</mo> <mi>a</mi> <mo stretchy="false">)</mo> <mi>cos</mi> <mo>&#x2061;<!-- ⁡ --></mo> <mo stretchy="false">(</mo> <mi>b</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sin(a+b)+\sin(a-b)=2\sin(a)\cos(b)\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec685b48682546f90bfdcde72f27636909f73171" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:39.541ex; height:2.843ex;" alt="{\displaystyle \sin(a+b)+\sin(a-b)=2\sin(a)\cos(b)\,}"></span></dd></dl> <p>Vi kan betrakta ekvationen som en ögonblicksbild av ett förlopp där vinklarna <i>a</i> och <i>b</i> ökar med olika hastighet med tiden. Varje sin- och cos-uttryck beskriver då en enkel <a href="/wiki/Harmonisk_sv%C3%A4ngning" class="mw-redirect" title="Harmonisk svängning">harmonisk svängning</a> mellan <a href="/wiki/Amplitud" title="Amplitud">amplitudvärdena</a> 1 och –1 där vinkeln inom parentesen beror på svängningens frekvens. </p><p>Antag att <i>a</i> motsvarar tonen 500&#160;Hz och <i>b</i> motsvarar 1&#160;Hz. Formelns vänsterled lägger i så fall samman tonerna 501&#160;Hz och 499&#160;Hz. Högerledet säger att detta lika gärna kan beskrivas som tonen 500&#160;Hz med dubbel styrka (faktorn 2) och ytterligare en faktor cos<i>(b)</i> som långsamt varierar tonstyrkan upp och ner i tiden och som utgör själva svävningen. </p><p>Faktorn cos<i>(b)</i> varierar här med frekvensen 1&#160;Hz. Men ljudstyrkan är som lägst när cos<i>(b)</i> passerar 0, och det sker två gånger under varje variation från 1 till –1 och tillbaka. Därför hör vi svävningen med 2&#160;Hz, vilket precis är skillnaden mellan tonerna 501&#160;Hz och 499&#160;Hz. </p><p>Samma ekvation kan i princip användas för att förklara (en kraftigt överstyrd) <a href="/wiki/Amplitudmodulering" title="Amplitudmodulering">amplitudmodulering</a>. Då måste man dock fysiskt modulera bärvågen <i>a</i> med svävningsfrekvensen <i>b</i> i en multiplikativ blandare för att åstadkomma 2 • sin<i>(a)</i> • cos<i>(b)</i>. Ekvationen säger att resultatet lika gärna kan uppfattas som en addition av två nya svängningar. Amplitudmodulering kräver alltså en olinjär signalprocess, medan svävning kan uppstå av sig själv så fort två olika signaler når en lyssnare samtidigt. </p> <div class="mw-heading mw-heading2"><h2 id="Är_svävning_modulation?"><span id=".C3.84r_sv.C3.A4vning_modulation.3F"></span>Är svävning modulation?</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Sv%C3%A4vning&amp;veaction=edit&amp;section=2" title="Redigera avsnitt: Är svävning modulation?" class="mw-editsection-visualeditor"><span>redigera</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Sv%C3%A4vning&amp;action=edit&amp;section=2" title="Redigera avsnitts källkod: Är svävning modulation?"><span>redigera wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Svaret kan vara både ja och nej, beroende på vad man lägger i ordet <a href="/wiki/Modulation" title="Modulation">modulation</a>. </p><p>Inom modulationsteorin har <i>modulation</i> en ganska snäv betydelse. Där ska en konstant bärvåg påverkas av en <a href="/wiki/Information" title="Information">informationsbärande</a> insignal i en <i>modulator</i> för att skapa en <a href="/wiki/Utsignal" title="Utsignal">utsignal</a> där <a href="/wiki/B%C3%A4rv%C3%A5g" title="Bärvåg">bärvågen</a> varierar i takt med <a href="/w/index.php?title=Insignal&amp;action=edit&amp;redlink=1" class="new" title="Insignal [inte skriven än]">insignalen</a>. Insignalen kan antingen påverka bärvågens <a href="/wiki/Amplitud" title="Amplitud">amplitud</a>, <a href="/wiki/Frekvens" title="Frekvens">frekvens</a> eller <a href="/wiki/Fas_(fysik,_ell%C3%A4ra)" class="mw-redirect" title="Fas (fysik, ellära)">fas</a>. En mottagare utnyttjar vetskapen om att bärvågen var konstant före modulationen och att all variation därför beror på den informationsbärande insignalen för att <i>demodulera</i> signalen och återskapa informationen. Man menar då med modulation den process som skapar den modulerade signalen. Enligt detta sysnätt är det svårt att se svävning som modulation. </p><p>Ett annat sätt att tolka modulation är att bara betrakta den signal man tar emot och analysera dess innehåll oavsett hur den kommit till. Modulation betraktas då inte som processen utan som den modulerade signalen. En svävning ser ut som en amplitudmodulerad signal. Även om den faktiskt åstadkommits genom att addera två toner, kunde den lika gärna ha skapats av en "bärvåg" som utgjorts av medeltonen och som bringats att ändra amplitud i takt med en "insignal" som motsvarat skillnaden mellan de toner vi faktiskt utgick ifrån. Enligt detta synsätt kan man alltså kalla svävning för modulation. Även betydligt mer komplexa signaler kan kallas modulerade om de uppvisar någon form av variation som har <a href="/wiki/Rytm" title="Rytm">rytm</a> eller annan struktur. Detta har tillämpningar inom <a href="/wiki/Akustik" title="Akustik">akustiken</a>. </p><p>Man kan slutligen tolka modulation som alla situationer där två <a href="/wiki/V%C3%A5gr%C3%B6relse" title="Vågrörelse">vågor</a> påverkar varandra så att en ny våg uppstår. Vid svävning räcker det då med att ta bort den ena tonen och konstatera att svävningen upphör för att visa att svävning är modulation i denna mening. </p> <div class="mw-heading mw-heading2"><h2 id="Se_även"><span id="Se_.C3.A4ven"></span>Se även</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Sv%C3%A4vning&amp;veaction=edit&amp;section=3" title="Redigera avsnitt: Se även" class="mw-editsection-visualeditor"><span>redigera</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Sv%C3%A4vning&amp;action=edit&amp;section=3" title="Redigera avsnitts källkod: Se även"><span>redigera wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Heterodynprincipen" title="Heterodynprincipen">Heterodynprincipen</a></li> <li><a href="/wiki/Intonering_av_gitarr" title="Intonering av gitarr">Intonering av gitarr</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Externa_länkar"><span id="Externa_l.C3.A4nkar"></span>Externa länkar</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Sv%C3%A4vning&amp;veaction=edit&amp;section=4" title="Redigera avsnitt: Externa länkar" class="mw-editsection-visualeditor"><span>redigera</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Sv%C3%A4vning&amp;action=edit&amp;section=4" title="Redigera avsnitts källkod: Externa länkar"><span>redigera wikitext</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><span typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/15px-Commons-logo.svg.png" decoding="async" width="15" height="20" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/23px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/30px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></span></span> Wikimedia Commons har media som rör <a href="https://commons.wikimedia.org/wiki/Category:Beat_frequencies" class="extiw" title="commons:Category:Beat frequencies">Svävning</a>.<div class="interProject commons" style="display:none;"><a href="https://commons.wikimedia.org/wiki/Category:Beat_frequencies" class="extiw" title="commons:Category:Beat frequencies">Bilder &amp; media</a></div></li></ul> <!-- NewPP limit report Parsed by mw‐web.eqiad.main‐6b6c9bdc8b‐p288h Cached time: 20241103185522 Cache expiry: 2592000 Reduced expiry: false Complications: [show‐toc] CPU time usage: 0.040 seconds Real time usage: 0.095 seconds Preprocessor visited node count: 62/1000000 Post‐expand include size: 409/2097152 bytes Template argument size: 48/2097152 bytes Highest expansion depth: 5/100 Expensive parser function count: 0/500 Unstrip recursion depth: 0/20 Unstrip post‐expand size: 36/5000000 bytes Lua time usage: 0.011/10.000 seconds Lua memory usage: 626942/52428800 bytes Number of Wikibase entities loaded: 1/400 --> <!-- Transclusion expansion time report (%,ms,calls,template) 100.00% 31.726 1 -total 100.00% 31.726 1 Mall:Commonscat 4.80% 1.522 1 Mall:Iwcommonscat --> <!-- Saved in parser cache with key svwiki:pcache:idhash:102474-0!canonical and timestamp 20241103185522 and revision id 55176324. 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