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id="toc-谐波与泛音的区别" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#谐波与泛音的区别"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>谐波与泛音的区别</span> </div> </a> <ul id="toc-谐波与泛音的区别-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-数学中的相关内容" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#数学中的相关内容"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>数学中的相关内容</span> </div> </a> <ul id="toc-数学中的相关内容-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-物理学中的相关内容" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#物理学中的相关内容"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>物理学中的相关内容</span> </div> </a> <ul id="toc-物理学中的相关内容-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="目录" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" title="目录" > <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="开关目录" > <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">开关目录</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">谐波</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="前往另一种语言写成的文章。32种语言可用" > <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-32" 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">32种语言</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%AA%D9%88%D8%A7%D9%81%D9%82" title="توافق – 阿拉伯语" lang="ar" hreflang="ar" data-title="توافق" data-language-autonym="العربية" data-language-local-name="阿拉伯语" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Harm%C3%B2nic" title="Harmònic – 加泰罗尼亚语" lang="ca" hreflang="ca" data-title="Harmònic" data-language-autonym="Català" data-language-local-name="加泰罗尼亚语" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Harmonische" title="Harmonische – 德语" lang="de" hreflang="de" data-title="Harmonische" data-language-autonym="Deutsch" data-language-local-name="德语" 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/Harmonic" title="Harmonic – 英语" lang="en" hreflang="en" data-title="Harmonic" data-language-autonym="English" data-language-local-name="英语" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Harmono" title="Harmono – 世界语" lang="eo" hreflang="eo" data-title="Harmono" data-language-autonym="Esperanto" data-language-local-name="世界语" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Arm%C3%B3nico" title="Armónico – 西班牙语" lang="es" hreflang="es" data-title="Armónico" data-language-autonym="Español" data-language-local-name="西班牙语" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Osahelid" title="Osahelid – 爱沙尼亚语" lang="et" hreflang="et" data-title="Osahelid" data-language-autonym="Eesti" data-language-local-name="爱沙尼亚语" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Harmoniko" title="Harmoniko – 巴斯克语" lang="eu" hreflang="eu" data-title="Harmoniko" data-language-autonym="Euskara" data-language-local-name="巴斯克语" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%87%D8%A7%D8%B1%D9%85%D9%88%D9%86%DB%8C%DA%A9" title="هارمونیک – 波斯语" lang="fa" hreflang="fa" data-title="هارمونیک" data-language-autonym="فارسی" data-language-local-name="波斯语" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Huilu%C3%A4%C3%A4ni" title="Huiluääni – 芬兰语" lang="fi" hreflang="fi" data-title="Huiluääni" data-language-autonym="Suomi" data-language-local-name="芬兰语" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Harmonique_(musique)" title="Harmonique (musique) – 法语" lang="fr" hreflang="fr" data-title="Harmonique (musique)" data-language-autonym="Français" data-language-local-name="法语" 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/Arm%C3%B3nach" title="Armónach – 爱尔兰语" lang="ga" hreflang="ga" data-title="Armónach" data-language-autonym="Gaeilge" data-language-local-name="爱尔兰语" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Harm%C3%B3nico" title="Harmónico – 加利西亚语" lang="gl" hreflang="gl" data-title="Harmónico" data-language-autonym="Galego" data-language-local-name="加利西亚语" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Pregib_(akustika)" title="Pregib (akustika) – 克罗地亚语" lang="hr" hreflang="hr" data-title="Pregib (akustika)" data-language-autonym="Hrvatski" data-language-local-name="克罗地亚语" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/Amoni" title="Amoni – 海地克里奥尔语" lang="ht" hreflang="ht" data-title="Amoni" data-language-autonym="Kreyòl ayisyen" data-language-local-name="海地克里奥尔语" class="interlanguage-link-target"><span>Kreyòl ayisyen</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Harmonisa" title="Harmonisa – 印度尼西亚语" lang="id" hreflang="id" data-title="Harmonisa" data-language-autonym="Bahasa Indonesia" data-language-local-name="印度尼西亚语" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Armonica_(fisica)" title="Armonica (fisica) – 意大利语" lang="it" hreflang="it" data-title="Armonica (fisica)" data-language-autonym="Italiano" data-language-local-name="意大利语" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E9%AB%98%E8%AA%BF%E6%B3%A2" title="高調波 – 日语" lang="ja" hreflang="ja" data-title="高調波" data-language-autonym="日本語" data-language-local-name="日语" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EA%B3%A0%EC%A1%B0%ED%8C%8C" title="고조파 – 韩语" lang="ko" hreflang="ko" data-title="고조파" data-language-autonym="한국어" data-language-local-name="韩语" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Harmonische" title="Harmonische – 荷兰语" lang="nl" hreflang="nl" data-title="Harmonische" data-language-autonym="Nederlands" data-language-local-name="荷兰语" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Harmonisk_b%C3%B8lgje" title="Harmonisk bølgje – 挪威尼诺斯克语" lang="nn" hreflang="nn" data-title="Harmonisk bølgje" data-language-autonym="Norsk nynorsk" data-language-local-name="挪威尼诺斯克语" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Armonica_(musica)" title="Armonica (musica) – 奥克语" lang="oc" hreflang="oc" data-title="Armonica (musica)" data-language-autonym="Occitan" data-language-local-name="奥克语" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Harmonika_(muzyka)" title="Harmonika (muzyka) – 波兰语" lang="pl" hreflang="pl" data-title="Harmonika (muzyka)" data-language-autonym="Polski" data-language-local-name="波兰语" 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/Harm%C3%B4nica" title="Harmônica – 葡萄牙语" lang="pt" hreflang="pt" data-title="Harmônica" data-language-autonym="Português" data-language-local-name="葡萄牙语" 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%93%D0%B0%D1%80%D0%BC%D0%BE%D0%BD%D0%B8%D0%BA%D0%B0_(%D0%BC%D1%83%D0%B7%D1%8B%D0%BA%D0%B0)" title="Гармоника (музыка) – 俄语" lang="ru" hreflang="ru" data-title="Гармоника (музыка)" data-language-autonym="Русский" data-language-local-name="俄语" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Alikvotni_tonovi" title="Alikvotni tonovi – 塞尔维亚-克罗地亚语" lang="sh" hreflang="sh" data-title="Alikvotni tonovi" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="塞尔维亚-克罗地亚语" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Harmonic" title="Harmonic – Simple English" lang="en-simple" hreflang="en-simple" data-title="Harmonic" 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/Fla%C5%BEolet" title="Flažolet – 斯洛文尼亚语" lang="sl" hreflang="sl" data-title="Flažolet" data-language-autonym="Slovenščina" data-language-local-name="斯洛文尼亚语" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%90%D0%BB%D0%B8%D0%BA%D0%B2%D0%BE%D1%82%D0%BD%D0%B8_%D1%82%D0%BE%D0%BD%D0%BE%D0%B2%D0%B8" title="Аликвотни тонови – 塞尔维亚语" lang="sr" hreflang="sr" data-title="Аликвотни тонови" data-language-autonym="Српски / srpski" data-language-local-name="塞尔维亚语" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Harmonisk_v%C3%A5g" title="Harmonisk våg – 瑞典语" lang="sv" hreflang="sv" data-title="Harmonisk våg" data-language-autonym="Svenska" data-language-local-name="瑞典语" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%AE%E0%B8%B2%E0%B8%A3%E0%B9%8C%E0%B8%A1%E0%B8%AD%E0%B8%99%E0%B8%B4%E0%B8%81" title="ฮาร์มอนิก – 泰语" lang="th" hreflang="th" data-title="ฮาร์มอนิก" data-language-autonym="ไทย" data-language-local-name="泰语" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%93%D0%B0%D1%80%D0%BC%D0%BE%D0%BD%D1%96%D0%BA%D0%B8" title="Гармоніки – 乌克兰语" lang="uk" hreflang="uk" data-title="Гармоніки" data-language-autonym="Українська" data-language-local-name="乌克兰语" class="interlanguage-link-target"><span>Українська</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/Q1148098#sitelinks-wikipedia" title="编辑跨语言链接" class="wbc-editpage">编辑链接</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div 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</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="页面工具"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="外观"> <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 vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">外观</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">移至侧栏</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">隐藏</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">维基百科，自由的百科全书</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="zh" dir="ltr"><style data-mw-deduplicate="TemplateStyles:r85100532">.mw-parser-output .hatnote{font-size:small}.mw-parser-output div.hatnote{padding-left:2em;margin-bottom:0.8em;margin-top:0.8em}.mw-parser-output .hatnote-notice-img::after{content:"\202f \202f \202f \202f "}.mw-parser-output .hatnote-notice-img-small::after{content:"\202f \202f "}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}body.skin-minerva .mw-parser-output .hatnote-notice-img,body.skin-minerva .mw-parser-output .hatnote-notice-img-small{display:none}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable"><span class="noviewer hatnote-notice-img" typeof="mw:File"><a href="/wiki/Wikipedia:%E6%B6%88%E6%AD%A7%E4%B9%89" title="Wikipedia:消歧义"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5f/Disambig_gray.svg/25px-Disambig_gray.svg.png" decoding="async" width="25" height="19" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5f/Disambig_gray.svg/38px-Disambig_gray.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5f/Disambig_gray.svg/50px-Disambig_gray.svg.png 2x" data-file-width="220" data-file-height="168" /></a></span>此条目的主題是数学物理学概念。关于電力系統中的同名概念，請見「<b><a href="/wiki/%E8%AB%A7%E6%B3%A2_(%E9%9B%BB%E5%8A%9B)" title="諧波 (電力)">諧波 (電力)</a></b>」。</div><style data-mw-deduplicate="TemplateStyles:r83732972">.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}html.client-js body.skin-minerva .mw-parser-output .mbox-text-span{margin-left:23px!important}@media(min-width:720px){.mw-parser-output .ambox{margin:0 10%}}@media screen{html.skin-theme-clientpref-night .mw-parser-output .ambox{border-left-color:#36c!important}html.skin-theme-clientpref-night .mw-parser-output .ambox-speedy,html.skin-theme-clientpref-night .mw-parser-output .ambox-delete{border-left-color:#b32424!important}html.skin-theme-clientpref-night .mw-parser-output .ambox-speedy{background-color:#300!important}html.skin-theme-clientpref-night .mw-parser-output .ambox-content{border-left-color:#f28500!important}html.skin-theme-clientpref-night .mw-parser-output .ambox-style{border-left-color:#fc3!important}html.skin-theme-clientpref-night .mw-parser-output .ambox-move{border-left-color:#9932cc!important}html.skin-theme-clientpref-night .mw-parser-output .ambox-protection{border-left-color:#a2a9b1!important}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .ambox{border-left-color:#36c!important}html.skin-theme-clientpref-os .mw-parser-output .ambox-speedy,html.skin-theme-clientpref-os .mw-parser-output .ambox-delete{border-left-color:#b32424!important}html.skin-theme-clientpref-os .mw-parser-output .ambox-speedy{background-color:#300!important}html.skin-theme-clientpref-os .mw-parser-output .ambox-content{border-left-color:#f28500!important}html.skin-theme-clientpref-os .mw-parser-output .ambox-style{border-left-color:#fc3!important}html.skin-theme-clientpref-os .mw-parser-output .ambox-move{border-left-color:#9932cc!important}html.skin-theme-clientpref-os .mw-parser-output .ambox-protection{border-left-color:#a2a9b1!important}}</style><table class="box-Expert_needed plainlinks metadata ambox ambox-content" role="presentation"><tbody><tr><td class="mbox-image"><div style="width:52px"><span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b4/Ambox_important.svg/40px-Ambox_important.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b4/Ambox_important.svg/60px-Ambox_important.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b4/Ambox_important.svg/80px-Ambox_important.svg.png 2x" data-file-width="40" data-file-height="40" /></span></span></div></td><td class="mbox-text"><div class="mbox-text-span">此條目需要<b>精通或熟悉相关主题的编者</b>参与及协助编辑。<span class="hide-when-compact"></span> <small class="date-container"><i>(<span class="date">2015年12月14日</span>)</i></small><span class="hide-when-compact"><br /><small>請<a href="/wiki/Wikipedia:%E5%B0%88%E5%AE%B6%E9%82%80%E8%AB%8B%E5%B7%A5%E4%BD%9C%E5%B0%8F%E7%B5%84" title="Wikipedia:專家邀請工作小組">邀請</a>適合的人士<a class="external text" href="https://zh.wikipedia.org/w/index.php?title=%E8%B0%90%E6%B3%A2&action=edit">改善本条目</a>。更多的細節與詳情請參见<a href="/wiki/Talk:%E8%B0%90%E6%B3%A2" title="Talk:谐波">討論頁</a>。</small></span><span class="hide-when-compact"></span></div></td></tr></tbody></table> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Moodswingerscale.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/2f/Moodswingerscale.svg/250px-Moodswingerscale.svg.png" decoding="async" width="250" height="277" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/2f/Moodswingerscale.svg/375px-Moodswingerscale.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/2f/Moodswingerscale.svg/500px-Moodswingerscale.svg.png 2x" data-file-width="512" data-file-height="568" /></a><figcaption>绳子抖动的模式是谐波</figcaption></figure> <p><b>谐波</b>是一个<a href="/wiki/%E6%95%B0%E5%AD%A6" title="数学">数学</a>或<a href="/wiki/%E7%89%A9%E7%90%86%E5%AD%A6" title="物理学">物理学</a>概念，是指<a href="/wiki/%E5%91%A8%E6%9C%9F%E5%87%BD%E6%95%B0" title="周期函数">周期函数</a>或周期性的<a href="/wiki/%E6%B3%A2" title="波">波</a>形中能用常数、与原函数的最小正周期相同的<a href="/wiki/%E6%AD%A3%E5%BC%A6%E5%87%BD%E6%95%B0" class="mw-redirect" title="正弦函数">正弦函数</a>和<a href="/wiki/%E4%BD%99%E5%BC%A6%E5%87%BD%E6%95%B0" class="mw-redirect" title="余弦函数">余弦函数</a>的<a href="/wiki/%E7%BA%BF%E6%80%A7%E7%BB%84%E5%90%88" title="线性组合">线性组合</a>表达的部分。 </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="周期性波形的展开"><span id=".E5.91.A8.E6.9C.9F.E6.80.A7.E6.B3.A2.E5.BD.A2.E7.9A.84.E5.B1.95.E5.BC.80"></span>周期性波形的展开</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E8%B0%90%E6%B3%A2&action=edit&section=1" title="编辑章节：周期性波形的展开"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>一般周期性波形不是完美的正弦函数或余弦函数，也就是说波形存在畸变，因此根据<a href="/wiki/%E5%82%85%E7%AB%8B%E5%8F%B6%E7%BA%A7%E6%95%B0" class="mw-redirect" title="傅立叶级数">傅立叶级数</a>的原理，周期函数都可以展开为常数与一组具有共同周期的正弦函数和余弦函数之和。<br /> 其展开式中，常数表达的部分称为<b>直流分量</b>，最小正周期等于原函数的周期的部分称为<b>基波</b>或<b>一次谐波</b>，最小正周期的若干倍等于原函数的周期的部分称为<b>高次谐波</b>。<br /> 因此高次谐波的<a href="/wiki/%E9%A0%BB%E7%8E%87_(%E7%89%A9%E7%90%86%E5%AD%B8)" title="頻率 (物理學)">频率</a>必然也等于基波的频率的若干倍，基波频率3倍的波称为<b>三次谐波</b>，基波频率5倍的波称为<b>五次谐波</b>，以此类推。不管几次谐波，他们都是<a href="/wiki/%E6%AD%A3%E5%BC%A6%E6%B3%A2" class="mw-redirect" title="正弦波">正弦波</a>。 </p> <div class="mw-heading mw-heading2"><h2 id="谐波与泛音的区别"><span id=".E8.B0.90.E6.B3.A2.E4.B8.8E.E6.B3.9B.E9.9F.B3.E7.9A.84.E5.8C.BA.E5.88.AB"></span>谐波与泛音的区别</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E8%B0%90%E6%B3%A2&action=edit&section=2" title="编辑章节：谐波与泛音的区别"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/%E6%B3%9B%E9%9F%B3" title="泛音">泛音</a>其实就是物理学上的谐波，但次数的定义稍许有些不同，基波频率2倍的音频称之为一次泛音，基波频率3倍的音频称之为二次泛音，以此类推。 </p> <div class="mw-heading mw-heading2"><h2 id="数学中的相关内容"><span id=".E6.95.B0.E5.AD.A6.E4.B8.AD.E7.9A.84.E7.9B.B8.E5.85.B3.E5.86.85.E5.AE.B9"></span>数学中的相关内容</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E8%B0%90%E6%B3%A2&action=edit&section=3" title="编辑章节：数学中的相关内容"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/%E5%82%85%E7%AB%8B%E5%8F%B6%E7%BA%A7%E6%95%B0" class="mw-redirect" title="傅立叶级数">傅立叶级数</a></li> <li><a href="/wiki/%E5%82%85%E7%AB%8B%E5%8F%B6%E5%8F%98%E6%8D%A2" class="mw-redirect" title="傅立叶变换">傅立叶变换</a></li> <li><a href="/wiki/%E4%B8%89%E8%A7%92%E5%87%BD%E6%95%B0" title="三角函数">三角函数</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="物理学中的相关内容"><span id=".E7.89.A9.E7.90.86.E5.AD.A6.E4.B8.AD.E7.9A.84.E7.9B.B8.E5.85.B3.E5.86.85.E5.AE.B9"></span>物理学中的相关内容</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E8%B0%90%E6%B3%A2&action=edit&section=4" title="编辑章节：物理学中的相关内容"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/%E6%96%B9%E6%B3%A2" title="方波">方波</a></li> <li><a href="/wiki/%E4%BD%8E%E9%80%9A%E6%BB%A4%E6%B3%A2%E5%99%A8" title="低通滤波器">低通滤波器</a></li> <li><a href="/wiki/%E6%8C%AF%E8%8D%A1%E5%99%A8" class="mw-redirect" title="振荡器">振荡器</a></li> <li><a href="/wiki/RLC%E7%94%B5%E8%B7%AF" title="RLC电路">RLC电路</a></li> <li><a href="/wiki/%E8%AB%A7%E6%B3%A2_(%E9%9B%BB%E5%8A%9B)" 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title="声学">声学</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%"><span class="ilh-all" data-orig-title="聲學工程" data-lang-code="en" data-lang-name="英语" data-foreign-title="Acoustical engineering"><span class="ilh-page"><a href="/w/index.php?title=%E8%81%B2%E5%AD%B8%E5%B7%A5%E7%A8%8B&action=edit&redlink=1" class="new" title="聲學工程（页面不存在）">聲學工程</a></span><span class="noprint ilh-comment"><span class="ilh-paren">（</span><span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Acoustical_engineering" class="extiw" title="en:Acoustical engineering"><span lang="en" dir="auto">Acoustical engineering</span></a></span><span class="ilh-paren">）</span></span></span></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E5%BB%BA%E7%AD%91%E5%A3%B0%E5%AD%A6" title="建筑声学">建筑声学</a></li> <li><a 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href="/w/index.php?title=%E5%BC%A6%E6%8C%AF%E8%8D%A1&action=edit&redlink=1" class="new" title="弦振荡（页面不存在）">弦振荡</a></span><span class="noprint ilh-comment"><span class="ilh-paren">（</span><span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/String_vibration" class="extiw" title="en:String vibration"><span lang="en" dir="auto">String vibration</span></a></span><span class="ilh-paren">）</span></span></span> <ul><li><span class="ilh-all" data-orig-title="弦共振" data-lang-code="en" data-lang-name="英语" data-foreign-title="string resonance"><span class="ilh-page"><a href="/w/index.php?title=%E5%BC%A6%E5%85%B1%E6%8C%AF&action=edit&redlink=1" class="new" title="弦共振（页面不存在）">弦共振</a></span><span class="noprint ilh-comment"><span class="ilh-paren">（</span><span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/string_resonance" class="extiw" title="en:string resonance"><span lang="en" dir="auto">string resonance</span></a></span><span class="ilh-paren">）</span></span></span></li></ul></li></ul> </div></td><td class="noviewer navbox-image" rowspan="5" style="width:1px;padding:0px 0px 0px 2px"><div><div class="plainlist"><ul><li><span typeof="mw:File"><a href="/wiki/File:Spectrogram_showing_shared_partials.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/26/Spectrogram_showing_shared_partials.png/80px-Spectrogram_showing_shared_partials.png" decoding="async" width="80" height="67" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/26/Spectrogram_showing_shared_partials.png/120px-Spectrogram_showing_shared_partials.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/26/Spectrogram_showing_shared_partials.png/160px-Spectrogram_showing_shared_partials.png 2x" data-file-width="300" data-file-height="250" /></a></span></li><li><span style="font-size:smaller;"><a href="/wiki/%E9%A2%91%E8%B0%B1" title="频谱">频谱图</a></span></li></ul></div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E5%A3%B0%E9%9F%B3" title="声音">声音</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E9%A0%BB%E7%8E%87_(%E7%89%A9%E7%90%86%E5%AD%B8)" title="頻率 (物理學)">頻率</a></li> <li><a href="/wiki/%E9%9F%B3%E9%AB%98" title="音高">音高</a> <ul><li><a href="/wiki/%E5%B7%B4%E5%85%8B%E5%88%BB%E5%BA%A6" title="巴克刻度">巴克刻度</a></li> <li><a href="/wiki/%E6%A2%85%E5%B0%94%E5%88%BB%E5%BA%A6" title="梅尔刻度">梅尔刻度</a></li></ul></li> <li><a href="/wiki/%E9%9F%B3%E8%B0%83" class="mw-redirect" title="音调">音调</a></li> <li><a href="/wiki/%E9%9F%B3%E8%89%B2" title="音色">音色</a></li> <li><a href="/wiki/%E6%8B%8D%E9%A2%91" title="拍频">拍频</a></li> <li><a href="/wiki/%E5%85%B1%E6%8C%AF%E5%B3%B0" title="共振峰">共振峰</a></li> <li><a href="/wiki/%E5%9F%BA%E6%9C%AC%E9%A0%BB%E7%8E%87" title="基本頻率">基本頻率</a></li> <li><a href="/wiki/%E9%A2%91%E8%B0%B1" title="频谱">频谱</a> <ul><li><a href="/wiki/%E8%AD%9C%E5%AF%86%E5%BA%A6" class="mw-redirect" title="譜密度">譜密度</a></li> <li><span class="ilh-all" data-orig-title="諧波頻譜" data-lang-code="en" data-lang-name="英语" data-foreign-title="Harmonic spectrum"><span class="ilh-page"><a href="/w/index.php?title=%E8%AB%A7%E6%B3%A2%E9%A0%BB%E8%AD%9C&action=edit&redlink=1" class="new" title="諧波頻譜（页面不存在）">諧波頻譜</a></span><span class="noprint ilh-comment"><span class="ilh-paren">（</span><span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Harmonic_spectrum" class="extiw" title="en:Harmonic spectrum"><span lang="en" dir="auto">Harmonic spectrum</span></a></span><span class="ilh-paren">）</span></span></span></li></ul></li> <li><a class="mw-selflink selflink">谐波</a> <ul><li><a href="/wiki/%E6%B3%9B%E9%9F%B3%E5%88%97" title="泛音列">泛音列</a></li> <li><a href="/wiki/%E5%81%8F%E5%B7%AE%E9%9F%B3" title="偏差音">偏差音</a></li> <li><a href="/wiki/%E6%B6%88%E5%A4%B1%E7%9A%84%E5%9F%BA%E9%A0%BB" title="消失的基頻">消失的基頻</a></li></ul></li> <li><a href="/wiki/%E6%B3%9B%E9%9F%B3" title="泛音">泛音</a></li> <li><span class="ilh-all" data-orig-title="音频共振" data-lang-code="en" data-lang-name="英语" data-foreign-title="Acoustic resonance"><span class="ilh-page"><a href="/w/index.php?title=%E9%9F%B3%E9%A2%91%E5%85%B1%E6%8C%AF&action=edit&redlink=1" class="new" title="音频共振（页面不存在）">音频共振</a></span><span class="noprint ilh-comment"><span class="ilh-paren">（</span><span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Acoustic_resonance" class="extiw" title="en:Acoustic resonance"><span lang="en" dir="auto">Acoustic resonance</span></a></span><span class="ilh-paren">）</span></span></span></li> <li><span class="ilh-all" data-orig-title="次諧波" data-lang-code="en" data-lang-name="英语" data-foreign-title="Subharmonic"><span class="ilh-page"><a href="/w/index.php?title=%E6%AC%A1%E8%AB%A7%E6%B3%A2&action=edit&redlink=1" class="new" title="次諧波（页面不存在）">次諧波</a></span><span class="noprint ilh-comment"><span class="ilh-paren">（</span><span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Subharmonic" class="extiw" title="en:Subharmonic"><span lang="en" dir="auto">Subharmonic</span></a></span><span class="ilh-paren">）</span></span></span></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">聲學家</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><span class="ilh-all" data-orig-title="延斯·布劳尔特" data-lang-code="en" data-lang-name="英语" data-foreign-title="Jens Blauert"><span class="ilh-page"><a href="/w/index.php?title=%E5%BB%B6%E6%96%AF%C2%B7%E5%B8%83%E5%8A%B3%E5%B0%94%E7%89%B9&action=edit&redlink=1" class="new" title="延斯·布劳尔特（页面不存在）">延斯·布劳尔特</a></span><span class="noprint ilh-comment"><span class="ilh-paren">（</span><span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Jens_Blauert" class="extiw" title="en:Jens Blauert"><span lang="en" dir="auto">Jens Blauert</span></a></span><span class="ilh-paren">）</span></span></span></li> <li><a href="/wiki/%E6%81%A9%E6%96%AF%E7%89%B9%C2%B7%E5%85%8B%E6%8B%89%E5%BE%B7%E5%B0%BC" title="恩斯特·克拉德尼">恩斯特·克拉德尼</a></li> <li><a href="/wiki/%E8%B5%AB%E5%B0%94%E6%9B%BC%C2%B7%E5%86%AF%C2%B7%E4%BA%A5%E5%A7%86%E9%9C%8D%E5%85%B9" title="赫尔曼·冯·亥姆霍兹">赫尔曼·冯·亥姆霍兹</a></li> <li><span class="ilh-all" data-orig-title="维尔纳·迈尔-埃普勒尔" data-lang-code="en" data-lang-name="英语" data-foreign-title="Werner Meyer-Eppler"><span class="ilh-page"><a href="/w/index.php?title=%E7%BB%B4%E5%B0%94%E7%BA%B3%C2%B7%E8%BF%88%E5%B0%94-%E5%9F%83%E6%99%AE%E5%8B%92%E5%B0%94&action=edit&redlink=1" class="new" title="维尔纳·迈尔-埃普勒尔（页面不存在）">维尔纳·迈尔-埃普勒尔</a></span><span class="noprint ilh-comment"><span class="ilh-paren">（</span><span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Werner_Meyer-Eppler" class="extiw" title="en:Werner Meyer-Eppler"><span lang="en" dir="auto">Werner Meyer-Eppler</span></a></span><span class="ilh-paren">）</span></span></span></li> <li><a href="/wiki/%E7%AC%AC%E4%B8%89%E4%BB%A3%E7%91%9E%E5%88%A9%E7%94%B7%E7%88%B5%E7%B4%84%E7%BF%B0%C2%B7%E6%96%AF%E7%89%B9%E6%8B%89%E7%89%B9" title="第三代瑞利男爵約翰·斯特拉特">約翰·斯特拉特，瑞利男爵III</a></li> <li><span class="ilh-all" data-orig-title="约瑟夫·索弗尔" data-lang-code="en" data-lang-name="英语" data-foreign-title="Joseph Sauveur"><span class="ilh-page"><a href="/w/index.php?title=%E7%BA%A6%E7%91%9F%E5%A4%AB%C2%B7%E7%B4%A2%E5%BC%97%E5%B0%94&action=edit&redlink=1" class="new" title="约瑟夫·索弗尔（页面不存在）">约瑟夫·索弗尔</a></span><span class="noprint ilh-comment"><span class="ilh-paren">（</span><span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Joseph_Sauveur" class="extiw" title="en:Joseph Sauveur"><span lang="en" dir="auto">Joseph Sauveur</span></a></span><span class="ilh-paren">）</span></span></span></li> <li><span class="ilh-all" data-orig-title="戴尔·万斯·霍利迪" data-lang-code="en" data-lang-name="英语" data-foreign-title="D. Van Holliday"><span class="ilh-page"><a href="/w/index.php?title=%E6%88%B4%E5%B0%94%C2%B7%E4%B8%87%E6%96%AF%C2%B7%E9%9C%8D%E5%88%A9%E8%BF%AA&action=edit&redlink=1" class="new" title="戴尔·万斯·霍利迪（页面不存在）">戴尔·万斯·霍利迪</a></span><span class="noprint ilh-comment"><span class="ilh-paren">（</span><span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/D._Van_Holliday" class="extiw" title="en:D. Van Holliday"><span lang="en" dir="auto">D. Van Holliday</span></a></span><span class="ilh-paren">）</span></span></span></li> <li><a href="/wiki/%E6%89%98%E9%A9%AC%E6%96%AF%C2%B7%E6%9D%A8" title="托马斯·杨">托马斯·杨</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">聲學分支</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E6%AC%A1%E5%A3%B0%E5%AD%A6" title="次声学">次声学</a></li> <li><a href="/wiki/%E8%B6%85%E5%A3%B0%E5%AD%A6" title="超声学">超声学</a></li> <li><a href="/wiki/%E9%87%8F%E5%AD%90%E5%A3%B0%E5%AD%A6" title="量子声学">量子声学</a></li> <li><a href="/wiki/%E9%9D%9E%E7%BA%BF%E6%80%A7%E5%A3%B0%E5%AD%A6" title="非线性声学">非线性声学</a></li> <li><a href="/wiki/%E8%AF%AD%E8%A8%80%E5%A3%B0%E5%AD%A6" title="语言声学">语言声学</a></li> <li><a href="/wiki/%E5%BF%83%E7%90%86%E5%A3%B0%E5%AD%A6" title="心理声学">心理声学</a></li> <li><a href="/wiki/%E5%9B%9E%E8%81%B2" title="回聲">回聲</a></li> <li><a href="/wiki/%E5%A3%B0%E6%B3%A2" title="声波">声波</a></li> <li><a href="/wiki/%E6%AC%A1%E5%A3%B0%E6%B3%A2" title="次声波">次声波</a></li> <li><a href="/wiki/%E8%B6%85%E8%81%B2%E6%B3%A2" title="超聲波">超聲波</a></li> <li><span class="ilh-all" data-orig-title="梅逊定律" data-lang-code="en" data-lang-name="英语" data-foreign-title="Mersenne's laws"><span class="ilh-page"><a href="/w/index.php?title=%E6%A2%85%E9%80%8A%E5%AE%9A%E5%BE%8B&action=edit&redlink=1" class="new" title="梅逊定律（页面不存在）">梅逊定律</a></span><span class="noprint ilh-comment"><span class="ilh-paren">（</span><span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Mersenne%27s_laws" class="extiw" title="en:Mersenne's laws"><span lang="en" dir="auto">Mersenne's laws</span></a></span><span class="ilh-paren">）</span></span></span></li> <li><a href="/wiki/%E9%9F%B3%E4%B9%90%E5%A3%B0%E5%AD%A6" title="音乐声学">音乐声学</a> <ul><li><a href="/wiki/%E5%B0%8F%E6%8F%90%E7%90%B4%E7%B5%90%E6%A7%8B" title="小提琴結構">小提琴</a></li></ul></li> <li><span class="ilh-all" data-orig-title="节点 (物理学)" data-lang-code="en" data-lang-name="英语" data-foreign-title="Node (physics)"><span class="ilh-page"><a href="/w/index.php?title=%E8%8A%82%E7%82%B9_(%E7%89%A9%E7%90%86%E5%AD%A6)&action=edit&redlink=1" class="new" title="节点 (物理学)（页面不存在）">节点 (物理学)</a></span><span class="noprint ilh-comment"><span class="ilh-paren">（</span><span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Node_(physics)" class="extiw" title="en:Node (physics)"><span lang="en" dir="auto">Node (physics)</span></a></span><span class="ilh-paren">）</span></span></span></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">聲學職業</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E9%9F%B3%E8%A8%8A%E5%B7%A5%E7%A8%8B%E5%B8%AB" title="音訊工程師">音訊工程師</a></li></ul> </div></td></tr><tr><td class="navbox-abovebelow hlist" colspan="3"><div> <ul><li><span typeof="mw:File"><span title="分类"><img alt="分类" src="//upload.wikimedia.org/wikipedia/commons/thumb/9/96/Symbol_category_class.svg/16px-Symbol_category_class.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/96/Symbol_category_class.svg/23px-Symbol_category_class.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/96/Symbol_category_class.svg/31px-Symbol_category_class.svg.png 2x" data-file-width="180" data-file-height="185" /></span></span> <a href="/wiki/Category:%E5%A3%B0%E5%AD%A6" title="Category:声学">聲學分類</a></li></ul> </div></td></tr></tbody></table></div> <table class="metadata plainlinks stub" role="presentation" style="background:transparent"><tbody><tr class="noresize"><td><span typeof="mw:File"><a href="/wiki/File:E-to-the-i-pi.svg" class="mw-file-description"><img alt="小作品圖示" src="//upload.wikimedia.org/wikipedia/commons/thumb/3/35/E-to-the-i-pi.svg/34px-E-to-the-i-pi.svg.png" decoding="async" width="34" height="30" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/35/E-to-the-i-pi.svg/51px-E-to-the-i-pi.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/35/E-to-the-i-pi.svg/68px-E-to-the-i-pi.svg.png 2x" data-file-width="512" data-file-height="453" /></a></span></td><td style="font-size:smaller">这是一篇关于数学的<a href="/wiki/Wikipedia:%E5%B0%8F%E4%BD%9C%E5%93%81" title="Wikipedia:小作品">小作品</a>。您可以通过<a class="external text" href="https://zh.wikipedia.org/w/index.php?title=%E8%B0%90%E6%B3%A2&action=edit">编辑或修订</a>扩充其内容。<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r84265675"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r84244141"><div class="navbar plainlinks hlist navbar-mini" style="position: absolute; right: 15px; display: none;"><ul><li class="nv-view"><a href="/wiki/Template:Math-stub" title="Template:Math-stub"><abbr title="查看该模板">查</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Math-stub" title="Template talk:Math-stub"><abbr title="讨论该模板">论</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:%E7%BC%96%E8%BE%91%E9%A1%B5%E9%9D%A2/Template:Math-stub" title="Special:编辑页面/Template:Math-stub"><abbr title="编辑该模板">编</abbr></a></li></ul></div></td></tr></tbody></table> <table class="metadata plainlinks stub" role="presentation" style="background:transparent"><tbody><tr class="noresize"><td><span typeof="mw:File"><a href="/wiki/File:Physics_template.svg" class="mw-file-description"><img alt="小作品圖示" src="//upload.wikimedia.org/wikipedia/commons/thumb/e/ee/Physics_template.svg/25px-Physics_template.svg.png" decoding="async" width="25" height="25" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/ee/Physics_template.svg/38px-Physics_template.svg.png 1.5x, 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