Sound pressure - Wikipedia

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<div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Sound measurements</span> </div> </a> <button aria-controls="toc-Sound_measurements-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Sound measurements subsection</span> </button> <ul id="toc-Sound_measurements-sublist" class="vector-toc-list"> <li id="toc-Sound_intensity" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Sound_intensity"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Sound intensity</span> </div> </a> <ul id="toc-Sound_intensity-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Acoustic_impedance" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Acoustic_impedance"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>Acoustic impedance</span> </div> </a> <ul id="toc-Acoustic_impedance-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Particle_displacement" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Particle_displacement"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3</span> <span>Particle displacement</span> </div> </a> <ul id="toc-Particle_displacement-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Inverse-proportional_law" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Inverse-proportional_law"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Inverse-proportional law</span> </div> </a> <ul id="toc-Inverse-proportional_law-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Sound_pressure_level" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Sound_pressure_level"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Sound pressure level</span> </div> </a> <button aria-controls="toc-Sound_pressure_level-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Sound pressure level subsection</span> </button> <ul id="toc-Sound_pressure_level-sublist" class="vector-toc-list"> <li id="toc-Examples" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Examples"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1</span> <span>Examples</span> </div> </a> <ul id="toc-Examples-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Distance" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Distance"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2</span> <span>Distance</span> </div> </a> <ul id="toc-Distance-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Multiple_sources" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Multiple_sources"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.3</span> <span>Multiple sources</span> </div> </a> <ul id="toc-Multiple_sources-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Examples_of_sound_pressure" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Examples_of_sound_pressure"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Examples of sound pressure</span> </div> </a> <ul id="toc-Examples_of_sound_pressure-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>External links</span> </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" 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class="mw-page-title-main">Sound pressure</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. 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href="https://bn.wikipedia.org/wiki/%E0%A6%B6%E0%A6%AC%E0%A7%8D%E0%A6%A6%E0%A6%9A%E0%A6%BE%E0%A6%AA" title="শব্দচাপ – Bangla" lang="bn" hreflang="bn" data-title="শব্দচাপ" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%97%D0%B2%D1%83%D0%BA%D0%BE%D0%B2%D0%BE_%D0%BD%D0%B0%D0%BB%D1%8F%D0%B3%D0%B0%D0%BD%D0%B5" title="Звуково налягане – Bulgarian" lang="bg" hreflang="bg" data-title="Звуково налягане" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bar mw-list-item"><a href="https://bar.wikipedia.org/wiki/Schoidruck" title="Schoidruck – Bavarian" lang="bar" hreflang="bar" data-title="Schoidruck" data-language-autonym="Boarisch" data-language-local-name="Bavarian" class="interlanguage-link-target"><span>Boarisch</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Pressi%C3%B3_sonora" title="Pressió sonora – Catalan" lang="ca" hreflang="ca" data-title="Pressió sonora" data-language-autonym="Català" data-language-local-name="Catalan" 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/Akustick%C3%BD_tlak" title="Akustický tlak – Czech" lang="cs" hreflang="cs" data-title="Akustický tlak" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Lydtryk" title="Lydtryk – Danish" lang="da" hreflang="da" data-title="Lydtryk" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Schalldruck" title="Schalldruck – German" lang="de" hreflang="de" data-title="Schalldruck" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Helir%C3%B5hk" title="Helirõhk – Estonian" lang="et" hreflang="et" data-title="Helirõhk" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Presi%C3%B3n_sonora" title="Presión sonora – Spanish" lang="es" hreflang="es" data-title="Presión sonora" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%81%D8%B4%D8%A7%D8%B1_%D8%B5%D8%AF%D8%A7" title="فشار صدا – Persian" lang="fa" hreflang="fa" data-title="فشار صدا" data-language-autonym="فارسی" data-language-local-name="Persian" 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/Pression_acoustique" title="Pression acoustique – French" lang="fr" hreflang="fr" data-title="Pression acoustique" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Presi%C3%B3n_sonora" title="Presión sonora – Galician" lang="gl" hreflang="gl" data-title="Presión sonora" data-language-autonym="Galego" data-language-local-name="Galician" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%9D%8C%EC%95%95" title="음압 – Korean" lang="ko" hreflang="ko" data-title="음압" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%81%D5%A1%D5%B5%D5%B6%D5%AB_%D5%B3%D5%B6%D5%B7%D5%B8%D6%82%D5%B4" title="Ձայնի ճնշում – Armenian" lang="hy" hreflang="hy" data-title="Ձայնի ճնշում" data-language-autonym="Հայերեն" data-language-local-name="Armenian" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Zvu%C4%8Dni_tlak" title="Zvučni tlak – Croatian" lang="hr" hreflang="hr" data-title="Zvučni tlak" data-language-autonym="Hrvatski" data-language-local-name="Croatian" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Tekanan_bunyi" title="Tekanan bunyi – Indonesian" lang="id" hreflang="id" data-title="Tekanan bunyi" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/SPL" title="SPL – Icelandic" lang="is" hreflang="is" data-title="SPL" data-language-autonym="Íslenska" data-language-local-name="Icelandic" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Pressione_acustica" title="Pressione acustica – Italian" lang="it" hreflang="it" data-title="Pressione acustica" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-lmo mw-list-item"><a href="https://lmo.wikipedia.org/wiki/Pression_son%C3%B2ra" title="Pression sonòra – Lombard" lang="lmo" hreflang="lmo" data-title="Pression sonòra" data-language-autonym="Lombard" data-language-local-name="Lombard" class="interlanguage-link-target"><span>Lombard</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Geluidsdruk" title="Geluidsdruk – Dutch" lang="nl" hreflang="nl" data-title="Geluidsdruk" data-language-autonym="Nederlands" data-language-local-name="Dutch" 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/%E9%9F%B3%E5%9C%A7" title="音圧 – Japanese" lang="ja" hreflang="ja" data-title="音圧" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Lydtrykk" title="Lydtrykk – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Lydtrykk" data-language-autonym="Norsk nynorsk" data-language-local-name="Norwegian Nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Ci%C5%9Bnienie_akustyczne" title="Ciśnienie akustyczne – Polish" lang="pl" hreflang="pl" data-title="Ciśnienie akustyczne" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Press%C3%A3o_sonora" title="Pressão sonora – Portuguese" lang="pt" hreflang="pt" data-title="Pressão sonora" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%97%D0%B2%D1%83%D0%BA%D0%BE%D0%B2%D0%BE%D0%B5_%D0%B4%D0%B0%D0%B2%D0%BB%D0%B5%D0%BD%D0%B8%D0%B5" title="Звуковое давление – Russian" lang="ru" hreflang="ru" data-title="Звуковое давление" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Zvo%C4%8Dni_tlak" title="Zvočni tlak – Slovenian" lang="sl" hreflang="sl" data-title="Zvočni tlak" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" 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/%C3%84%C3%A4nenpaine" title="Äänenpaine – Finnish" lang="fi" hreflang="fi" data-title="Äänenpaine" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Ljudniv%C3%A5" title="Ljudnivå – Swedish" lang="sv" hreflang="sv" data-title="Ljudnivå" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%97%D0%B2%D1%83%D0%BA%D0%BE%D0%B2%D0%B8%D0%B9_%D1%82%D0%B8%D1%81%D0%BA" title="Звуковий тиск – Ukrainian" lang="uk" hreflang="uk" data-title="Звуковий тиск" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a 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searchaux" style="display:none">Local pressure deviation caused by a sound wave</div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">Not to be confused with <a href="/wiki/Sound_energy_density" title="Sound energy density">Sound energy density</a>.</div> <style data-mw-deduplicate="TemplateStyles:r1257001546">.mw-parser-output .infobox-subbox{padding:0;border:none;margin:-3px;width:auto;min-width:100%;font-size:100%;clear:none;float:none;background-color:transparent}.mw-parser-output .infobox-3cols-child{margin:auto}.mw-parser-output .infobox .navbar{font-size:100%}@media screen{html.skin-theme-clientpref-night .mw-parser-output .infobox-full-data:not(.notheme)>div:not(.notheme)[style]{background:#1f1f23!important;color:#f8f9fa}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .infobox-full-data:not(.notheme) div:not(.notheme){background:#1f1f23!important;color:#f8f9fa}}@media(min-width:640px){body.skin--responsive .mw-parser-output .infobox-table{display:table!important}body.skin--responsive .mw-parser-output .infobox-table>caption{display:table-caption!important}body.skin--responsive .mw-parser-output .infobox-table>tbody{display:table-row-group}body.skin--responsive .mw-parser-output .infobox-table tr{display:table-row!important}body.skin--responsive .mw-parser-output .infobox-table th,body.skin--responsive .mw-parser-output .infobox-table td{padding-left:inherit;padding-right:inherit}}</style><table class="infobox" style="width:19.0em;"><tbody><tr><th colspan="2" class="infobox-above" style="background:#ccf;padding:0.3em;font-size:125%;">Sound measurements</th></tr><tr><th scope="row" class="infobox-label" style="font-weight:normal;"><div style="background:#ddf;padding:0.15em 0.5em;">Characteristic</div></th><td class="infobox-data"><div style="background:#ddf;padding:0.15em 0.5em;">Symbols</div></td></tr><tr><th scope="row" class="infobox-label" style="font-weight:normal;"><span style="padding-left:0.3em;"> </span><a class="mw-selflink selflink">Sound pressure</a></th><td class="infobox-data"><span style="padding-left:0.3em;"> </span><span class="texhtml"><i>p</i>, SPL, <i>L</i><sub>PA</sub></span></td></tr><tr><th scope="row" class="infobox-label" style="font-weight:normal;"><span style="padding-left:0.3em;"> </span><a href="/wiki/Particle_velocity" title="Particle velocity">Particle velocity</a></th><td class="infobox-data"><span style="padding-left:0.3em;"> </span><span class="texhtml"><i>v</i>, SVL</span></td></tr><tr><th scope="row" class="infobox-label" style="font-weight:normal;"><span style="padding-left:0.3em;"> </span><a href="/wiki/Particle_displacement" title="Particle displacement">Particle displacement</a></th><td class="infobox-data"><span style="padding-left:0.3em;"> </span><span class="texhtml mvar" style="font-style:italic;">δ</span></td></tr><tr><th scope="row" class="infobox-label" style="font-weight:normal;"><span style="padding-left:0.3em;"> </span><a href="/wiki/Sound_intensity" title="Sound intensity">Sound intensity</a></th><td class="infobox-data"><span style="padding-left:0.3em;"> </span><span class="texhtml"><i>I</i>, SIL</span></td></tr><tr><th scope="row" class="infobox-label" style="font-weight:normal;"><span style="padding-left:0.3em;"> </span><a href="/wiki/Sound_power" title="Sound power">Sound power</a></th><td class="infobox-data"><span style="padding-left:0.3em;"> </span><span class="texhtml"><i>P</i>, SWL, <i>L</i><sub>WA</sub></span></td></tr><tr><th scope="row" class="infobox-label" style="font-weight:normal;"><span style="padding-left:0.3em;"> </span><a href="/wiki/Sound_energy" title="Sound energy">Sound energy</a></th><td class="infobox-data"><span style="padding-left:0.3em;"> </span><span class="texhtml mvar" style="font-style:italic;">W</span></td></tr><tr><th scope="row" class="infobox-label" style="font-weight:normal;"><span style="padding-left:0.3em;"> </span><a href="/wiki/Sound_energy_density" title="Sound energy density">Sound energy density</a></th><td class="infobox-data"><span style="padding-left:0.3em;"> </span><span class="texhtml mvar" style="font-style:italic;">w</span></td></tr><tr><th scope="row" class="infobox-label" style="font-weight:normal;"><span style="padding-left:0.3em;"> </span><a href="/wiki/Sound_exposure" title="Sound exposure">Sound exposure</a></th><td class="infobox-data"><span style="padding-left:0.3em;"> </span><span class="texhtml"><i>E</i>, SEL</span></td></tr><tr><th scope="row" class="infobox-label" style="font-weight:normal;"><span style="padding-left:0.3em;"> </span><a href="/wiki/Acoustic_impedance" title="Acoustic impedance">Acoustic impedance</a></th><td class="infobox-data"><span style="padding-left:0.3em;"> </span><span class="texhtml mvar" style="font-style:italic;">Z</span></td></tr><tr><th scope="row" class="infobox-label" style="font-weight:normal;"><span style="padding-left:0.3em;"> </span><a href="/wiki/Audio_frequency" title="Audio frequency">Audio frequency</a></th><td class="infobox-data"><span style="padding-left:0.3em;"> </span><span class="texhtml">AF</span></td></tr><tr><th scope="row" class="infobox-label" style="font-weight:normal;"><span style="padding-left:0.3em;"> </span><a href="/wiki/Transmission_loss_(duct_acoustics)" title="Transmission loss (duct acoustics)">Transmission loss</a></th><td class="infobox-data"><span style="padding-left:0.3em;"> </span><span class="texhtml">TL</span></td></tr><tr><td colspan="2" class="infobox-full-data"><hr /></td></tr><tr><td colspan="2" class="infobox-navbar"><style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output .hlist ol ul,.mw-parser-output .hlist ul dl,.mw-parser-output .hlist ul ol,.mw-parser-output .hlist ul ul{display:inline}.mw-parser-output .hlist .mw-empty-li{display:none}.mw-parser-output .hlist dt::after{content:": "}.mw-parser-output .hlist dd::after,.mw-parser-output .hlist li::after{content:" · ";font-weight:bold}.mw-parser-output .hlist dd:last-child::after,.mw-parser-output .hlist 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li:last-child::after{content:")";font-weight:normal}.mw-parser-output .hlist ol{counter-reset:listitem}.mw-parser-output .hlist ol>li{counter-increment:listitem}.mw-parser-output .hlist ol>li::before{content:" "counter(listitem)"\a0 "}.mw-parser-output .hlist dd ol>li:first-child::before,.mw-parser-output .hlist dt ol>li:first-child::before,.mw-parser-output .hlist li ol>li:first-child::before{content:" ("counter(listitem)"\a0 "}</style><style data-mw-deduplicate="TemplateStyles:r1239400231">.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}html.skin-theme-clientpref-night .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Sound_measurements" title="Template:Sound measurements"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Sound_measurements" title="Template talk:Sound measurements"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Sound_measurements" title="Special:EditPage/Template:Sound measurements"><abbr title="Edit this template">e</abbr></a></li></ul></div></td></tr></tbody></table> <p><b>Sound pressure</b> or <b>acoustic pressure</b> is the local <a href="/wiki/Pressure" title="Pressure">pressure</a> deviation from the ambient (average or equilibrium) <a href="/wiki/Atmospheric_pressure" title="Atmospheric pressure">atmospheric pressure</a>, caused by a <a href="/wiki/Sound_wave" class="mw-redirect" title="Sound wave">sound wave</a>. In air, sound pressure can be measured using a <a href="/wiki/Microphone" title="Microphone">microphone</a>, and in water with a <a href="/wiki/Hydrophone" title="Hydrophone">hydrophone</a>. The <a href="/wiki/International_System_of_Units" title="International System of Units">SI unit</a> of sound pressure is the <a href="/wiki/Pascal_(unit)" title="Pascal (unit)">pascal</a> (Pa).<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Mathematical_definition">Mathematical definition</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Sound_pressure&action=edit&section=1" title="Edit section: Mathematical definition"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Sound_pressure_diagram.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/7a/Sound_pressure_diagram.svg/240px-Sound_pressure_diagram.svg.png" decoding="async" width="240" height="121" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/7a/Sound_pressure_diagram.svg/360px-Sound_pressure_diagram.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/7a/Sound_pressure_diagram.svg/480px-Sound_pressure_diagram.svg.png 2x" data-file-width="861" data-file-height="433" /></a><figcaption>Sound pressure diagram: <div><ol><li>Silence</li><li>Audible sound</li><li>Atmospheric pressure</li><li>Sound pressure</li></ol></div></figcaption></figure> <p>A sound wave in a <a href="/wiki/Transmission_medium" title="Transmission medium">transmission medium</a> causes a deviation (sound pressure, a <i>dynamic</i> pressure) in the local ambient pressure, a <i>static</i> pressure. </p><p>Sound pressure, denoted <i>p</i>, is defined by <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p_{\text{total}}=p_{\text{stat}}+p,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>total</mtext> </mrow> </msub> <mo>=</mo> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>stat</mtext> </mrow> </msub> <mo>+</mo> <mi>p</mi> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p_{\text{total}}=p_{\text{stat}}+p,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4ff32c2d212a8ca8fab68732b1ff3ffa5cda1866" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:16.778ex; height:2.343ex;" alt="{\displaystyle p_{\text{total}}=p_{\text{stat}}+p,}"></span> where </p> <ul><li><i>p</i><sub>total</sub> is the total pressure,</li> <li><i>p</i><sub>stat</sub> is the static pressure.</li></ul> <div class="mw-heading mw-heading2"><h2 id="Sound_measurements">Sound measurements</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Sound_pressure&action=edit&section=2" title="Edit section: Sound measurements"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Sound_intensity">Sound intensity</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Sound_pressure&action=edit&section=3" title="Edit section: Sound intensity"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Sound_intensity" title="Sound intensity">Sound intensity</a></div> <p>In a sound wave, the complementary variable to sound pressure is the <a href="/wiki/Particle_velocity" title="Particle velocity">particle velocity</a>. Together, they determine the sound intensity of the wave. </p><p><i>Sound intensity</i>, denoted <b>I</b> and measured in <a href="/wiki/Watt" title="Watt">W</a>·<a href="/wiki/Metre" title="Metre">m</a><sup>−2</sup> in SI units, is defined by <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {I} =p\mathbf {v} ,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">I</mi> </mrow> <mo>=</mo> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {I} =p\mathbf {v} ,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cfb735583e04d53382a8bbe844b9622f08bca2cb" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.34ex; height:2.509ex;" alt="{\displaystyle \mathbf {I} =p\mathbf {v} ,}"></span> where </p> <ul><li><i>p</i> is the sound pressure,</li> <li><b>v</b> is the particle velocity.</li></ul> <div class="mw-heading mw-heading3"><h3 id="Acoustic_impedance">Acoustic impedance</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Sound_pressure&action=edit&section=4" title="Edit section: Acoustic impedance"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Acoustic_impedance" title="Acoustic impedance">Acoustic impedance</a></div> <p><i>Acoustic impedance</i>, denoted <i>Z</i> and measured in Pa·m<sup>−3</sup>·s in SI units, is defined by<sup id="cite_ref-Wolfe_2-0" class="reference"><a href="#cite_note-Wolfe-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle Z(s)={\frac {{\hat {p}}(s)}{{\hat {Q}}(s)}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Z</mi> <mo stretchy="false">(</mo> <mi>s</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>p</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mo stretchy="false">(</mo> <mi>s</mi> <mo stretchy="false">)</mo> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>Q</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mo stretchy="false">(</mo> <mi>s</mi> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Z(s)={\frac {{\hat {p}}(s)}{{\hat {Q}}(s)}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/084e59522c540f0d2026d03d54474c900395f59f" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:13.9ex; height:7.009ex;" alt="{\displaystyle Z(s)={\frac {{\hat {p}}(s)}{{\hat {Q}}(s)}},}"></span> where </p> <ul><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\hat {p}}(s)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>p</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mo stretchy="false">(</mo> <mi>s</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\hat {p}}(s)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/234fb5abd7d45b29fe2732868c0d5db979622bf0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-left: -0.089ex; width:4.349ex; height:2.843ex;" alt="{\displaystyle {\hat {p}}(s)}"></span> is the <a href="/wiki/Laplace_transform" title="Laplace transform">Laplace transform</a> of sound pressure,<sup class="noprint Inline-Template Template-Fact" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Citation_needed" title="Wikipedia:Citation needed"><span title="This claim needs references to reliable sources. (April 2015)">citation needed</span></a></i>]</sup></li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\hat {Q}}(s)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>Q</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mo stretchy="false">(</mo> <mi>s</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\hat {Q}}(s)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1daaacc1b1650d90c77f062efc0655be4be6af31" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.738ex; height:3.343ex;" alt="{\displaystyle {\hat {Q}}(s)}"></span> is the Laplace transform of sound volume flow rate.</li></ul> <p><i>Specific acoustic impedance</i>, denoted <i>z</i> and measured in Pa·m<sup>−1</sup>·s in SI units, is defined by<sup id="cite_ref-Wolfe_2-1" class="reference"><a href="#cite_note-Wolfe-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle z(s)={\frac {{\hat {p}}(s)}{{\hat {v}}(s)}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>z</mi> <mo stretchy="false">(</mo> <mi>s</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>p</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mo stretchy="false">(</mo> <mi>s</mi> <mo stretchy="false">)</mo> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>v</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mo stretchy="false">(</mo> <mi>s</mi> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle z(s)={\frac {{\hat {p}}(s)}{{\hat {v}}(s)}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/18ce1aba96c204f4b7f7e7cc577250dc6e63f127" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:12.828ex; height:6.509ex;" alt="{\displaystyle z(s)={\frac {{\hat {p}}(s)}{{\hat {v}}(s)}},}"></span> where </p> <ul><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\hat {p}}(s)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>p</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mo stretchy="false">(</mo> <mi>s</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\hat {p}}(s)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/234fb5abd7d45b29fe2732868c0d5db979622bf0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-left: -0.089ex; width:4.349ex; height:2.843ex;" alt="{\displaystyle {\hat {p}}(s)}"></span> is the Laplace transform of sound pressure,</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\hat {v}}(s)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>v</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mo stretchy="false">(</mo> <mi>s</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\hat {v}}(s)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0273fcda7aeed9818ac1dcbdb6a2fb54cd62df26" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.127ex; height:2.843ex;" alt="{\displaystyle {\hat {v}}(s)}"></span> is the Laplace transform of particle velocity.</li></ul> <div class="mw-heading mw-heading3"><h3 id="Particle_displacement">Particle displacement</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Sound_pressure&action=edit&section=5" title="Edit section: Particle displacement"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Particle_displacement" title="Particle displacement">Particle displacement</a></div> <p>The <i>particle displacement</i> of a <i>progressive <a href="/wiki/Sine_wave" title="Sine wave">sine wave</a></i> is given by <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \delta (\mathbf {r} ,t)=\delta _{\text{m}}\cos(\mathbf {k} \cdot \mathbf {r} -\omega t+\varphi _{\delta ,0}),}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>δ</mi> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mo>,</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>=</mo> <msub> <mi>δ</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>m</mtext> </mrow> </msub> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">k</mi> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mo>−</mo> <mi>ω</mi> <mi>t</mi> <mo>+</mo> <msub> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>δ</mi> <mo>,</mo> <mn>0</mn> </mrow> </msub> <mo stretchy="false">)</mo> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \delta (\mathbf {r} ,t)=\delta _{\text{m}}\cos(\mathbf {k} \cdot \mathbf {r} -\omega t+\varphi _{\delta ,0}),}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0e2ecd7d4fa13100f38e5334489fad0d82f30bf0" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:33.452ex; height:3.009ex;" alt="{\displaystyle \delta (\mathbf {r} ,t)=\delta _{\text{m}}\cos(\mathbf {k} \cdot \mathbf {r} -\omega t+\varphi _{\delta ,0}),}"></span> where </p> <ul><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \delta _{\text{m}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>δ</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>m</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \delta _{\text{m}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/21b42106c9554620c48db3901917f0bb37aac570" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.634ex; height:2.676ex;" alt="{\displaystyle \delta _{\text{m}}}"></span> is the <a href="/wiki/Amplitude" title="Amplitude">amplitude</a> of the particle displacement,</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \varphi _{\delta ,0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>δ</mi> <mo>,</mo> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \varphi _{\delta ,0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5906b40b69752f745ea656f26a87e7b8c7ab9296" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:3.773ex; height:2.343ex;" alt="{\displaystyle \varphi _{\delta ,0}}"></span> is the <a href="/wiki/Phase_shift" class="mw-redirect" title="Phase shift">phase shift</a> of the particle displacement,</li> <li><b>k</b> is the <a href="/wiki/Angular_wavevector" class="mw-redirect" title="Angular wavevector">angular wavevector</a>,</li> <li><i>ω</i> is the <a href="/wiki/Angular_frequency" title="Angular frequency">angular frequency</a>.</li></ul> <p>It follows that the particle velocity and the sound pressure along the direction of propagation of the sound wave <i>x</i> are given by <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v(\mathbf {r} ,t)={\frac {\partial \delta }{\partial t}}(\mathbf {r} ,t)=\omega \delta _{\text{m}}\cos \left(\mathbf {k} \cdot \mathbf {r} -\omega t+\varphi _{\delta ,0}+{\frac {\pi }{2}}\right)=v_{\text{m}}\cos(\mathbf {k} \cdot \mathbf {r} -\omega t+\varphi _{v,0}),}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>v</mi> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mo>,</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>δ</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mo>,</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>ω</mi> <msub> <mi>δ</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>m</mtext> </mrow> </msub> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">k</mi> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mo>−</mo> <mi>ω</mi> <mi>t</mi> <mo>+</mo> <msub> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>δ</mi> <mo>,</mo> <mn>0</mn> </mrow> </msub> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>π</mi> <mn>2</mn> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>m</mtext> </mrow> </msub> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">k</mi> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mo>−</mo> <mi>ω</mi> <mi>t</mi> <mo>+</mo> <msub> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>v</mi> <mo>,</mo> <mn>0</mn> </mrow> </msub> <mo stretchy="false">)</mo> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v(\mathbf {r} ,t)={\frac {\partial \delta }{\partial t}}(\mathbf {r} ,t)=\omega \delta _{\text{m}}\cos \left(\mathbf {k} \cdot \mathbf {r} -\omega t+\varphi _{\delta ,0}+{\frac {\pi }{2}}\right)=v_{\text{m}}\cos(\mathbf {k} \cdot \mathbf {r} -\omega t+\varphi _{v,0}),}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/24d1f7b51ef41624e759231ac1176050c5c851e7" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:79.159ex; height:5.509ex;" alt="{\displaystyle v(\mathbf {r} ,t)={\frac {\partial \delta }{\partial t}}(\mathbf {r} ,t)=\omega \delta _{\text{m}}\cos \left(\mathbf {k} \cdot \mathbf {r} -\omega t+\varphi _{\delta ,0}+{\frac {\pi }{2}}\right)=v_{\text{m}}\cos(\mathbf {k} \cdot \mathbf {r} -\omega t+\varphi _{v,0}),}"></span> <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p(\mathbf {r} ,t)=-\rho c^{2}{\frac {\partial \delta }{\partial x}}(\mathbf {r} ,t)=\rho c^{2}k_{x}\delta _{\text{m}}\cos \left(\mathbf {k} \cdot \mathbf {r} -\omega t+\varphi _{\delta ,0}+{\frac {\pi }{2}}\right)=p_{\text{m}}\cos(\mathbf {k} \cdot \mathbf {r} -\omega t+\varphi _{p,0}),}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mo>,</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mo>−</mo> <mi>ρ</mi> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂</mi> <mi>δ</mi> </mrow> <mrow> <mi mathvariant="normal">∂</mi> <mi>x</mi> </mrow> </mfrac> </mrow> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mo>,</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>ρ</mi> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> <msub> <mi>δ</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>m</mtext> </mrow> </msub> <mi>cos</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">k</mi> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mo>−</mo> <mi>ω</mi> <mi>t</mi> <mo>+</mo> <msub> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>δ</mi> <mo>,</mo> <mn>0</mn> </mrow> </msub> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>π</mi> <mn>2</mn> </mfrac> </mrow> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>m</mtext> </mrow> </msub> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">k</mi> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mo>−</mo> <mi>ω</mi> <mi>t</mi> <mo>+</mo> <msub> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> <mo>,</mo> <mn>0</mn> </mrow> </msub> <mo stretchy="false">)</mo> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p(\mathbf {r} ,t)=-\rho c^{2}{\frac {\partial \delta }{\partial x}}(\mathbf {r} ,t)=\rho c^{2}k_{x}\delta _{\text{m}}\cos \left(\mathbf {k} \cdot \mathbf {r} -\omega t+\varphi _{\delta ,0}+{\frac {\pi }{2}}\right)=p_{\text{m}}\cos(\mathbf {k} \cdot \mathbf {r} -\omega t+\varphi _{p,0}),}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2efb633d18128f22d152898ddeb1d35e8618072a" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; margin-left: -0.089ex; width:88.915ex; height:5.509ex;" alt="{\displaystyle p(\mathbf {r} ,t)=-\rho c^{2}{\frac {\partial \delta }{\partial x}}(\mathbf {r} ,t)=\rho c^{2}k_{x}\delta _{\text{m}}\cos \left(\mathbf {k} \cdot \mathbf {r} -\omega t+\varphi _{\delta ,0}+{\frac {\pi }{2}}\right)=p_{\text{m}}\cos(\mathbf {k} \cdot \mathbf {r} -\omega t+\varphi _{p,0}),}"></span> where </p> <ul><li><i>v</i><sub>m</sub> is the amplitude of the particle velocity,</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \varphi _{v,0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>v</mi> <mo>,</mo> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \varphi _{v,0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fd7e4fec8b39505d691c094571f5e52183eb83af" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:3.829ex; height:2.343ex;" alt="{\displaystyle \varphi _{v,0}}"></span> is the phase shift of the particle velocity,</li> <li><i>p</i><sub>m</sub> is the amplitude of the acoustic pressure,</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \varphi _{p,0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> <mo>,</mo> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \varphi _{p,0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4eb8787b976b68c67541cbeddd4994acbdd78e5a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:3.859ex; height:2.343ex;" alt="{\displaystyle \varphi _{p,0}}"></span> is the phase shift of the acoustic pressure.</li></ul> <p>Taking the Laplace transforms of <i>v</i> and <i>p</i> with respect to time yields <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\hat {v}}(\mathbf {r} ,s)=v_{\text{m}}{\frac {s\cos \varphi _{v,0}-\omega \sin \varphi _{v,0}}{s^{2}+\omega ^{2}}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>v</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mo>,</mo> <mi>s</mi> <mo stretchy="false">)</mo> <mo>=</mo> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>m</mtext> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>s</mi> <mi>cos</mi> <mo>⁡</mo> <msub> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>v</mi> <mo>,</mo> <mn>0</mn> </mrow> </msub> <mo>−</mo> <mi>ω</mi> <mi>sin</mi> <mo>⁡</mo> <msub> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>v</mi> <mo>,</mo> <mn>0</mn> </mrow> </msub> </mrow> <mrow> <msup> <mi>s</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\hat {v}}(\mathbf {r} ,s)=v_{\text{m}}{\frac {s\cos \varphi _{v,0}-\omega \sin \varphi _{v,0}}{s^{2}+\omega ^{2}}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5526fa1d846c03d0cb7aee8639c2294364a7206a" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:34.123ex; height:6.009ex;" alt="{\displaystyle {\hat {v}}(\mathbf {r} ,s)=v_{\text{m}}{\frac {s\cos \varphi _{v,0}-\omega \sin \varphi _{v,0}}{s^{2}+\omega ^{2}}},}"></span> <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\hat {p}}(\mathbf {r} ,s)=p_{\text{m}}{\frac {s\cos \varphi _{p,0}-\omega \sin \varphi _{p,0}}{s^{2}+\omega ^{2}}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>p</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mo>,</mo> <mi>s</mi> <mo stretchy="false">)</mo> <mo>=</mo> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>m</mtext> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>s</mi> <mi>cos</mi> <mo>⁡</mo> <msub> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> <mo>,</mo> <mn>0</mn> </mrow> </msub> <mo>−</mo> <mi>ω</mi> <mi>sin</mi> <mo>⁡</mo> <msub> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> <mo>,</mo> <mn>0</mn> </mrow> </msub> </mrow> <mrow> <msup> <mi>s</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\hat {p}}(\mathbf {r} ,s)=p_{\text{m}}{\frac {s\cos \varphi _{p,0}-\omega \sin \varphi _{p,0}}{s^{2}+\omega ^{2}}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a6fb9279fd73f389bb8f47c5b93f4e74f0ffba45" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; margin-left: -0.089ex; width:34.446ex; height:6.009ex;" alt="{\displaystyle {\hat {p}}(\mathbf {r} ,s)=p_{\text{m}}{\frac {s\cos \varphi _{p,0}-\omega \sin \varphi _{p,0}}{s^{2}+\omega ^{2}}}.}"></span> </p><p>Since <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 \varphi _{v,0}=\varphi _{p,0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>v</mi> <mo>,</mo> <mn>0</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>φ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> <mo>,</mo> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \varphi _{v,0}=\varphi _{p,0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b353d586a60cd236185ece7285e7040e1dfb40e4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:10.786ex; height:2.343ex;" alt="{\displaystyle \varphi _{v,0}=\varphi _{p,0}}"></span>, the amplitude of the specific acoustic impedance is given by <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle z_{\text{m}}(\mathbf {r} ,s)=|z(\mathbf {r} ,s)|=\left|{\frac {{\hat {p}}(\mathbf {r} ,s)}{{\hat {v}}(\mathbf {r} ,s)}}\right|={\frac {p_{\text{m}}}{v_{\text{m}}}}={\frac {\rho c^{2}k_{x}}{\omega }}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>m</mtext> </mrow> </msub> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mo>,</mo> <mi>s</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>z</mi> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mo>,</mo> <mi>s</mi> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mo>=</mo> <mrow> <mo>|</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>p</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mo>,</mo> <mi>s</mi> <mo stretchy="false">)</mo> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>v</mi> <mo stretchy="false">^</mo> </mover> </mrow> </mrow> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mo>,</mo> <mi>s</mi> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> <mo>|</mo> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>m</mtext> </mrow> </msub> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>m</mtext> </mrow> </msub> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>ρ</mi> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> </mrow> <mi>ω</mi> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle z_{\text{m}}(\mathbf {r} ,s)=|z(\mathbf {r} ,s)|=\left|{\frac {{\hat {p}}(\mathbf {r} ,s)}{{\hat {v}}(\mathbf {r} ,s)}}\right|={\frac {p_{\text{m}}}{v_{\text{m}}}}={\frac {\rho c^{2}k_{x}}{\omega }}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d63181c1508474dceb43b3cd60a4c273ba00430c" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:46.791ex; height:6.509ex;" alt="{\displaystyle z_{\text{m}}(\mathbf {r} ,s)=|z(\mathbf {r} ,s)|=\left|{\frac {{\hat {p}}(\mathbf {r} ,s)}{{\hat {v}}(\mathbf {r} ,s)}}\right|={\frac {p_{\text{m}}}{v_{\text{m}}}}={\frac {\rho c^{2}k_{x}}{\omega }}.}"></span> </p><p>Consequently, the amplitude of the particle displacement is related to that of the acoustic velocity and the sound pressure by <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \delta _{\text{m}}={\frac {v_{\text{m}}}{\omega }},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>δ</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>m</mtext> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>m</mtext> </mrow> </msub> <mi>ω</mi> </mfrac> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \delta _{\text{m}}={\frac {v_{\text{m}}}{\omega }},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/067f0cf4d44e56ffd6b9efda42cea79cae1feac9" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:9.944ex; height:4.676ex;" alt="{\displaystyle \delta _{\text{m}}={\frac {v_{\text{m}}}{\omega }},}"></span> <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \delta _{\text{m}}={\frac {p_{\text{m}}}{\omega z_{\text{m}}(\mathbf {r} ,s)}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>δ</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>m</mtext> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>m</mtext> </mrow> </msub> <mrow> <mi>ω</mi> <msub> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>m</mtext> </mrow> </msub> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">r</mi> </mrow> <mo>,</mo> <mi>s</mi> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \delta _{\text{m}}={\frac {p_{\text{m}}}{\omega z_{\text{m}}(\mathbf {r} ,s)}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fd3dd6482dd266fc63a70ae4327870285ce09534" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:16.379ex; height:5.676ex;" alt="{\displaystyle \delta _{\text{m}}={\frac {p_{\text{m}}}{\omega z_{\text{m}}(\mathbf {r} ,s)}}.}"></span> </p> <div class="mw-heading mw-heading2"><h2 id="Inverse-proportional_law">Inverse-proportional law</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Sound_pressure&action=edit&section=6" title="Edit section: Inverse-proportional law"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Further information: <a href="/wiki/Inverse-square_law" title="Inverse-square law">Inverse-square law</a></div> <p>When measuring the sound pressure created by a sound source, it is important to measure the distance from the object as well, since the sound pressure of a <i>spherical</i> sound wave decreases as 1/<i>r</i> from the centre of the sphere (and not as 1/<i>r</i><sup>2</sup>, like the <a href="/wiki/Sound_intensity" title="Sound intensity">sound intensity</a>):<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p(r)\propto {\frac {1}{r}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> <mo stretchy="false">(</mo> <mi>r</mi> <mo stretchy="false">)</mo> <mo>∝</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>r</mi> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p(r)\propto {\frac {1}{r}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/da6333429beabd7bfe76a9aec5db4170be8897d8" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; margin-left: -0.089ex; width:9.861ex; height:5.176ex;" alt="{\displaystyle p(r)\propto {\frac {1}{r}}.}"></span> </p><p>This relationship is an <i>inverse-proportional law</i>. </p><p>If the sound pressure <i>p</i><sub>1</sub> is measured at a distance <i>r</i><sub>1</sub> from the centre of the sphere, the sound pressure <i>p</i><sub>2</sub> at another position <i>r</i><sub>2</sub> can be calculated: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p_{2}={\frac {r_{1}}{r_{2}}}\,p_{1}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mfrac> </mrow> <mspace width="thinmathspace" /> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p_{2}={\frac {r_{1}}{r_{2}}}\,p_{1}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c6f3e2b8735c308bee9df6f9d54195fd178ab2c9" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; margin-left: -0.089ex; width:11.608ex; height:5.009ex;" alt="{\displaystyle p_{2}={\frac {r_{1}}{r_{2}}}\,p_{1}.}"></span> </p><p>The inverse-proportional law for sound pressure comes from the inverse-square law for <a href="/wiki/Sound_intensity" title="Sound intensity">sound intensity</a>: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle I(r)\propto {\frac {1}{r^{2}}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>I</mi> <mo stretchy="false">(</mo> <mi>r</mi> <mo stretchy="false">)</mo> <mo>∝</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I(r)\propto {\frac {1}{r^{2}}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/39f123726ff0b863f6d2bfe3de065ec48bfdf4cc" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:10.714ex; height:5.509ex;" alt="{\displaystyle I(r)\propto {\frac {1}{r^{2}}}.}"></span> Indeed, <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle I(r)=p(r)v(r)=p(r)\left[p*z^{-1}\right](r)\propto p^{2}(r),}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>I</mi> <mo stretchy="false">(</mo> <mi>r</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>p</mi> <mo stretchy="false">(</mo> <mi>r</mi> <mo stretchy="false">)</mo> <mi>v</mi> <mo stretchy="false">(</mo> <mi>r</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>p</mi> <mo stretchy="false">(</mo> <mi>r</mi> <mo stretchy="false">)</mo> <mrow> <mo>[</mo> <mrow> <mi>p</mi> <mo>∗</mo> <msup> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> <mo>]</mo> </mrow> <mo stretchy="false">(</mo> <mi>r</mi> <mo stretchy="false">)</mo> <mo>∝</mo> <msup> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo stretchy="false">(</mo> <mi>r</mi> <mo stretchy="false">)</mo> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I(r)=p(r)v(r)=p(r)\left[p*z^{-1}\right](r)\propto p^{2}(r),}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bf101a3713c0641e63e2093d8d2c8f2bb424264d" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:43.453ex; height:3.343ex;" alt="{\displaystyle I(r)=p(r)v(r)=p(r)\left[p*z^{-1}\right](r)\propto p^{2}(r),}"></span> where </p> <ul><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>v</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e07b00e7fc0847fbd16391c778d65bc25c452597" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.128ex; height:1.676ex;" alt="{\displaystyle v}"></span> is the particle velocity,</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle *}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∗</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle *}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8e9972f426d9e07855984f73ee195a21dbc21755" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: 0.079ex; margin-bottom: -0.25ex; width:1.162ex; height:1.509ex;" alt="{\displaystyle *}"></span> is the <a href="/wiki/Convolution" title="Convolution">convolution</a> operator,</li> <li><i>z</i><sup>−1</sup> is the convolution inverse of the <a href="/wiki/Specific_acoustic_impedance" class="mw-redirect" title="Specific acoustic impedance">specific acoustic impedance</a>,</li></ul> <p>hence the inverse-proportional law: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p(r)\propto {\frac {1}{r}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> <mo stretchy="false">(</mo> <mi>r</mi> <mo stretchy="false">)</mo> <mo>∝</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>r</mi> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p(r)\propto {\frac {1}{r}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/da6333429beabd7bfe76a9aec5db4170be8897d8" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; margin-left: -0.089ex; width:9.861ex; height:5.176ex;" alt="{\displaystyle p(r)\propto {\frac {1}{r}}.}"></span> </p> <div class="mw-heading mw-heading2"><h2 id="Sound_pressure_level">Sound pressure level</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Sound_pressure&action=edit&section=7" title="Edit section: Sound pressure level"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">For other uses, see <a href="/wiki/Sound_level_(disambiguation)" class="mw-redirect mw-disambig" title="Sound level (disambiguation)">Sound level</a>.</div> <p><b>Sound pressure level</b> (<b>SPL</b>) or <b>acoustic pressure level</b> (<b>APL</b>) is a <a href="/wiki/Level_(logarithmic_quantity)" title="Level (logarithmic quantity)">logarithmic measure</a> of the effective pressure of a sound relative to a reference value. </p><p>Sound pressure level, denoted <i>L</i><sub><i>p</i></sub> and measured in <a href="/wiki/Decibel" title="Decibel">dB</a>,<sup id="cite_ref-IEC60027-3_4-0" class="reference"><a href="#cite_note-IEC60027-3-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> is defined by:<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle L_{p}=\ln \left({\frac {p}{p_{0}}}\right)~{\text{Np}}=2\log _{10}\left({\frac {p}{p_{0}}}\right)~{\text{B}}=20\log _{10}\left({\frac {p}{p_{0}}}\right)~{\text{dB}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> <mo>=</mo> <mi>ln</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>p</mi> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mfrac> </mrow> <mo>)</mo> </mrow> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mtext>Np</mtext> </mrow> <mo>=</mo> <mn>2</mn> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>10</mn> </mrow> </msub> <mo>⁡</mo> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>p</mi> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mfrac> </mrow> <mo>)</mo> </mrow> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mtext>B</mtext> </mrow> <mo>=</mo> <mn>20</mn> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>10</mn> </mrow> </msub> <mo>⁡</mo> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>p</mi> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mfrac> </mrow> <mo>)</mo> </mrow> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mtext>dB</mtext> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L_{p}=\ln \left({\frac {p}{p_{0}}}\right)~{\text{Np}}=2\log _{10}\left({\frac {p}{p_{0}}}\right)~{\text{B}}=20\log _{10}\left({\frac {p}{p_{0}}}\right)~{\text{dB}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9080618dde646db8ae9cf5bf9dbe66b49d8ed175" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:57.285ex; height:6.176ex;" alt="{\displaystyle L_{p}=\ln \left({\frac {p}{p_{0}}}\right)~{\text{Np}}=2\log _{10}\left({\frac {p}{p_{0}}}\right)~{\text{B}}=20\log _{10}\left({\frac {p}{p_{0}}}\right)~{\text{dB}},}"></span> where </p> <ul><li><i>p</i> is the <a href="/wiki/Root_mean_square" title="Root mean square">root mean square</a> sound pressure,<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup></li> <li><i>p</i><sub>0</sub> is a <b>reference sound pressure</b>,</li> <li><span class="nowrap">1 Np</span> is the <a href="/wiki/Neper" title="Neper">neper</a>,</li> <li><span class="nowrap">1 B = (<style data-mw-deduplicate="TemplateStyles:r1214402035">.mw-parser-output .sfrac{white-space:nowrap}.mw-parser-output .sfrac.tion,.mw-parser-output .sfrac .tion{display:inline-block;vertical-align:-0.5em;font-size:85%;text-align:center}.mw-parser-output .sfrac .num{display:block;line-height:1em;margin:0.0em 0.1em;border-bottom:1px solid}.mw-parser-output .sfrac .den{display:block;line-height:1em;margin:0.1em 0.1em}.mw-parser-output .sr-only{border:0;clip:rect(0,0,0,0);clip-path:polygon(0px 0px,0px 0px,0px 0px);height:1px;margin:-1px;overflow:hidden;padding:0;position:absolute;width:1px}</style><span class="sfrac">⁠<span class="tion"><span class="num">1</span><span class="sr-only">/</span><span class="den">2</span></span>⁠</span> ln 10) Np</span> is the <a href="/wiki/Decibel" title="Decibel">bel</a>,</li> <li><span class="nowrap">1 dB = (<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1214402035"><span class="sfrac">⁠<span class="tion"><span class="num">1</span><span class="sr-only">/</span><span class="den">20</span></span>⁠</span> ln 10) Np</span> is the <a href="/wiki/Decibel" title="Decibel">decibel</a>.</li></ul> <p><span class="anchor" id="Reference"></span>The commonly used reference sound pressure in air is<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p> <style data-mw-deduplicate="TemplateStyles:r996643573">.mw-parser-output .block-indent{padding-left:3em;padding-right:0;overflow:hidden}</style><div class="block-indent" style="padding-left: 1.5em;"><i>p</i><sub>0</sub> = 20 μPa,</div> <p>which is often considered as the <a href="/wiki/Threshold_of_human_hearing" class="mw-redirect" title="Threshold of human hearing">threshold of human hearing</a> (roughly the sound of a mosquito flying 3 m away). The proper notations for sound pressure level using this reference are <span class="nowrap"><i>L</i><sub><i>p</i>/(20 μPa)</sub></span> or <span class="nowrap"><i>L</i><sub><i>p</i></sub> (re 20 μPa)</span>, but the suffix notations <span class="nowrap">dB SPL</span>, <span class="nowrap">dB(SPL)</span>, dBSPL, and dB<sub>SPL</sub> are very common, even if they are not accepted by the SI.<sup id="cite_ref-NIST2008_8-0" class="reference"><a href="#cite_note-NIST2008-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> </p><p>Most sound-level measurements will be made relative to this reference, meaning <span class="nowrap">1 Pa</span> will equal an SPL of <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 20\log _{10}\left({\frac {1}{2\times 10^{-5}}}\right)~{\text{dB}}\approx 94~{\text{dB}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>20</mn> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>10</mn> </mrow> </msub> <mo>⁡</mo> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mn>2</mn> <mo>×</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>5</mn> </mrow> </msup> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mtext>dB</mtext> </mrow> <mo>≈</mo> <mn>94</mn> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mtext>dB</mtext> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 20\log _{10}\left({\frac {1}{2\times 10^{-5}}}\right)~{\text{dB}}\approx 94~{\text{dB}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e673156f55cfcb13f80a8fdbfbd14535d7beff6c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:32.939ex; height:6.176ex;" alt="{\displaystyle 20\log _{10}\left({\frac {1}{2\times 10^{-5}}}\right)~{\text{dB}}\approx 94~{\text{dB}}}"></span>. In other media, such as <a href="/wiki/Underwater_acoustics" title="Underwater acoustics">underwater</a>, a reference level of <span class="nowrap">1 μPa</span> is used.<sup id="cite_ref-Morfey_9-0" class="reference"><a href="#cite_note-Morfey-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> These references are defined in <a href="/wiki/American_National_Standards_Institute" title="American National Standards Institute">ANSI</a> <a href="/wiki/ANSI/ASA_S1.1-2013" title="ANSI/ASA S1.1-2013">S1.1-2013</a>.<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> </p><p>The main instrument for measuring sound levels in the environment is the <a href="/wiki/Sound_level_meter" title="Sound level meter">sound level meter</a>. Most sound level meters provide readings in A, C, and Z-weighted decibels and must meet international standards such as <a href="/wiki/IEC_61672" class="mw-redirect" title="IEC 61672">IEC 61672-2013</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Examples">Examples</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Sound_pressure&action=edit&section=8" title="Edit section: Examples"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The lower limit of audibility is defined as SPL of <span class="nowrap">0 dB</span>, but the upper limit is not as clearly defined. While <span class="nowrap">1 <a href="/wiki/Atmosphere_(unit)" class="mw-redirect" title="Atmosphere (unit)">atm</a></span> (<span class="nowrap">194 dB peak</span> or <span class="nowrap">191 dB SPL</span>)<sup id="cite_ref-:0_11-0" class="reference"><a href="#cite_note-:0-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-:1_12-0" class="reference"><a href="#cite_note-:1-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> is the largest pressure variation an undistorted sound wave can have in <a href="/wiki/Earth%27s_atmosphere" class="mw-redirect" title="Earth's atmosphere">Earth's atmosphere</a> (i. e., if the thermodynamic properties of the air are disregarded; in reality, the sound waves become progressively non-linear starting over 150 dB), larger sound waves can be present in other <a href="/wiki/Atmosphere" title="Atmosphere">atmospheres</a> or other media, such as underwater or through the Earth.<sup id="cite_ref-Audio1_13-0" class="reference"><a href="#cite_note-Audio1-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Lindos1.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/47/Lindos1.svg/240px-Lindos1.svg.png" decoding="async" width="240" height="215" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/47/Lindos1.svg/360px-Lindos1.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/47/Lindos1.svg/480px-Lindos1.svg.png 2x" data-file-width="704" data-file-height="632" /></a><figcaption><a href="/wiki/Equal-loudness_contour" title="Equal-loudness contour">Equal-loudness contour</a>, showing sound-pressure-vs-frequency at different perceived loudness levels</figcaption></figure> <p>Ears detect changes in sound pressure. Human hearing does not have a flat <a href="/wiki/Spectral_sensitivity" title="Spectral sensitivity">spectral sensitivity</a> (<a href="/wiki/Frequency_response" title="Frequency response">frequency response</a>) relative to frequency versus <a href="/wiki/Amplitude" title="Amplitude">amplitude</a>. Humans do not perceive low- and high-frequency sounds as well as they perceive sounds between 3,000 and 4,000 Hz, as shown in the <a href="/wiki/Equal-loudness_contour" title="Equal-loudness contour">equal-loudness contour</a>. Because the frequency response of human hearing changes with amplitude, three weightings have been established for measuring sound pressure: A, B and C. </p><p>In order to distinguish the different sound measures, a suffix is used: A-weighted sound pressure level is written either as dB<sub>A</sub> or L<sub>A</sub>. B-weighted sound pressure level is written either as dB<sub>B</sub> or L<sub>B</sub>, and C-weighted sound pressure level is written either as dB<sub>C</sub> or L<sub>C</sub>. Unweighted sound pressure level is called "linear sound pressure level" and is often written as dB<sub>L</sub> or just L. Some sound measuring instruments use the letter "Z" as an indication of linear SPL.<sup id="cite_ref-Audio1_13-1" class="reference"><a href="#cite_note-Audio1-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Distance">Distance</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Sound_pressure&action=edit&section=9" title="Edit section: Distance"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The distance of the measuring microphone from a sound source is often omitted when SPL measurements are quoted, making the data useless, due to the inherent effect of the <a href="#Inverse-proportional_law">inverse proportional law</a>. In the case of ambient environmental measurements of "background" noise, distance need not be quoted, as no single source is present, but when measuring the noise level of a specific piece of equipment, the distance should always be stated. A distance of one <a href="/wiki/Metre" title="Metre">metre</a> (1 m) from the source is a frequently used standard distance. Because of the effects of reflected noise within a closed room, the use of an <a href="/wiki/Anechoic_chamber" title="Anechoic chamber">anechoic chamber</a> allows sound to be comparable to measurements made in a free field environment.<sup id="cite_ref-Audio1_13-2" class="reference"><a href="#cite_note-Audio1-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> </p><p>According to the inverse proportional law, when sound level <i>L</i><sub><i>p</i><sub>1</sub></sub> is measured at a distance <i>r</i><sub>1</sub>, the sound level <i>L</i><sub><i>p</i><sub>2</sub></sub> at the distance <i>r</i><sub>2</sub> is <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle L_{p_{2}}=L_{p_{1}}+20\log _{10}\left({\frac {r_{1}}{r_{2}}}\right)~{\text{dB}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </msub> <mo>=</mo> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mrow> </msub> <mo>+</mo> <mn>20</mn> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>10</mn> </mrow> </msub> <mo>⁡</mo> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mfrac> </mrow> <mo>)</mo> </mrow> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mtext>dB</mtext> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L_{p_{2}}=L_{p_{1}}+20\log _{10}\left({\frac {r_{1}}{r_{2}}}\right)~{\text{dB}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e0b334b0639c248a36129e21fb8d569d72858d25" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:30.972ex; height:6.176ex;" alt="{\displaystyle L_{p_{2}}=L_{p_{1}}+20\log _{10}\left({\frac {r_{1}}{r_{2}}}\right)~{\text{dB}}.}"></span> </p> <div class="mw-heading mw-heading3"><h3 id="Multiple_sources">Multiple sources</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Sound_pressure&action=edit&section=10" title="Edit section: Multiple sources"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The formula for the sum of the sound pressure levels of <i>n</i> incoherent radiating sources is <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle L_{\Sigma }=10\log _{10}\left({\frac {p_{1}^{2}+p_{2}^{2}+\dots +p_{n}^{2}}{p_{0}^{2}}}\right)~{\text{dB}}=10\log _{10}\left[\left({\frac {p_{1}}{p_{0}}}\right)^{2}+\left({\frac {p_{2}}{p_{0}}}\right)^{2}+\dots +\left({\frac {p_{n}}{p_{0}}}\right)^{2}\right]~{\text{dB}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Σ</mi> </mrow> </msub> <mo>=</mo> <mn>10</mn> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>10</mn> </mrow> </msub> <mo>⁡</mo> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msubsup> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>+</mo> <msubsup> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mo>+</mo> <mo>⋯</mo> <mo>+</mo> <msubsup> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> </mrow> <msubsup> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> </mfrac> </mrow> <mo>)</mo> </mrow> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mtext>dB</mtext> </mrow> <mo>=</mo> <mn>10</mn> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>10</mn> </mrow> </msub> <mo>⁡</mo> <mrow> <mo>[</mo> <mrow> <msup> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mo>⋯</mo> <mo>+</mo> <msup> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mo>]</mo> </mrow> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mtext>dB</mtext> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L_{\Sigma }=10\log _{10}\left({\frac {p_{1}^{2}+p_{2}^{2}+\dots +p_{n}^{2}}{p_{0}^{2}}}\right)~{\text{dB}}=10\log _{10}\left[\left({\frac {p_{1}}{p_{0}}}\right)^{2}+\left({\frac {p_{2}}{p_{0}}}\right)^{2}+\dots +\left({\frac {p_{n}}{p_{0}}}\right)^{2}\right]~{\text{dB}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2c430352c5808ad08cb5bb81221d3058efd94d2d" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:91.325ex; height:7.509ex;" alt="{\displaystyle L_{\Sigma }=10\log _{10}\left({\frac {p_{1}^{2}+p_{2}^{2}+\dots +p_{n}^{2}}{p_{0}^{2}}}\right)~{\text{dB}}=10\log _{10}\left[\left({\frac {p_{1}}{p_{0}}}\right)^{2}+\left({\frac {p_{2}}{p_{0}}}\right)^{2}+\dots +\left({\frac {p_{n}}{p_{0}}}\right)^{2}\right]~{\text{dB}}.}"></span> </p><p>Inserting the formulas <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left({\frac {p_{i}}{p_{0}}}\right)^{2}=10^{\frac {L_{i}}{10~{\text{dB}}}},\quad i=1,2,\ldots ,n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mrow> <mn>10</mn> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mtext>dB</mtext> </mrow> </mrow> </mfrac> </mrow> </msup> <mo>,</mo> <mspace width="1em" /> <mi>i</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mo>…</mo> <mo>,</mo> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left({\frac {p_{i}}{p_{0}}}\right)^{2}=10^{\frac {L_{i}}{10~{\text{dB}}}},\quad i=1,2,\ldots ,n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2270893d2821d35a7b921172fe133ddddc2f9293" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:34.818ex; height:6.509ex;" alt="{\displaystyle \left({\frac {p_{i}}{p_{0}}}\right)^{2}=10^{\frac {L_{i}}{10~{\text{dB}}}},\quad i=1,2,\ldots ,n}"></span> in the formula for the sum of the sound pressure levels yields <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle L_{\Sigma }=10\log _{10}\left(10^{\frac {L_{1}}{10~{\text{dB}}}}+10^{\frac {L_{2}}{10~{\text{dB}}}}+\dots +10^{\frac {L_{n}}{10~{\text{dB}}}}\right)~{\text{dB}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Σ</mi> </mrow> </msub> <mo>=</mo> <mn>10</mn> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>10</mn> </mrow> </msub> <mo>⁡</mo> <mrow> <mo>(</mo> <mrow> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mrow> <mn>10</mn> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mtext>dB</mtext> </mrow> </mrow> </mfrac> </mrow> </msup> <mo>+</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mrow> <mn>10</mn> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mtext>dB</mtext> </mrow> </mrow> </mfrac> </mrow> </msup> <mo>+</mo> <mo>⋯</mo> <mo>+</mo> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mrow> <mn>10</mn> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mtext>dB</mtext> </mrow> </mrow> </mfrac> </mrow> </msup> </mrow> <mo>)</mo> </mrow> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mtext>dB</mtext> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L_{\Sigma }=10\log _{10}\left(10^{\frac {L_{1}}{10~{\text{dB}}}}+10^{\frac {L_{2}}{10~{\text{dB}}}}+\dots +10^{\frac {L_{n}}{10~{\text{dB}}}}\right)~{\text{dB}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/291f776da7b1d1a3cc021e53a9773b85b06ce7f4" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:53.477ex; height:6.176ex;" alt="{\displaystyle L_{\Sigma }=10\log _{10}\left(10^{\frac {L_{1}}{10~{\text{dB}}}}+10^{\frac {L_{2}}{10~{\text{dB}}}}+\dots +10^{\frac {L_{n}}{10~{\text{dB}}}}\right)~{\text{dB}}.}"></span> </p> <div class="mw-heading mw-heading2"><h2 id="Examples_of_sound_pressure">Examples of sound pressure</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Sound_pressure&action=edit&section=11" title="Edit section: Examples of sound pressure"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <table class="wikitable sortable"> <caption>Examples of sound pressure in air at <a href="/wiki/Standard_atmosphere_(unit)" title="Standard atmosphere (unit)">standard atmospheric pressure</a> </caption> <tbody><tr> <th rowspan="2">Source of sound </th> <th rowspan="2">Distance </th> <th colspan="2">Sound pressure level<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>a<span class="cite-bracket">]</span></a></sup> </th></tr> <tr> <th>(<a href="/wiki/Pascal_(unit)" title="Pascal (unit)">Pa</a>) </th> <th>(<a href="/wiki/Decibel" title="Decibel">dB<sub>SPL</sub></a>) </th></tr> <tr> <td><a href="/wiki/Shock_wave" title="Shock wave">Shock wave</a> (distorted sound waves > 1 <a href="/wiki/Atmosphere_(unit)" class="mw-redirect" title="Atmosphere (unit)">atm</a>; waveform valleys are clipped at zero pressure)<sup id="cite_ref-:0_11-1" class="reference"><a href="#cite_note-:0-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-:1_12-1" class="reference"><a href="#cite_note-:1-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> </td> <td> </td> <td align="right">>1.01×10<sup>5</sup> </td> <td align="right">>191 </td></tr> <tr> <td>Simple open-ended <a href="/wiki/Thermoacoustics" title="Thermoacoustics">thermoacoustic</a> device<sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup> </td> <td><sup class="noprint Inline-Template" style="margin-left:0.1em; white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Please_clarify" title="Wikipedia:Please clarify"><span title="The text near this tag may need clarification or removal of jargon. (January 2016)">clarification needed</span></a></i>]</sup> </td> <td align="right">1.26×10<sup>4</sup> </td> <td align="right">176 </td></tr> <tr> <td><a href="/wiki/1883_eruption_of_Krakatoa" title="1883 eruption of Krakatoa">1883 eruption of Krakatoa</a><sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-winchester_17-0" class="reference"><a href="#cite_note-winchester-17"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> </td> <td>165 km </td> <td> </td> <td align="right">172 </td></tr> <tr> <td><a href="/wiki/.30-06_Springfield" title=".30-06 Springfield">.30-06 rifle</a> being fired </td> <td>1 <a href="/wiki/Meter" class="mw-redirect" title="Meter">m</a> to<br />shooter's side </td> <td align="right">7.09×10<sup>3</sup> </td> <td align="right">171 </td></tr> <tr> <td>Firecracker<sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup> </td> <td>0.5 m </td> <td align="right">7.09×10<sup>3</sup> </td> <td align="right">171 </td></tr> <tr> <td><a href="/wiki/Stun_grenade" title="Stun grenade">Stun grenade</a><sup id="cite_ref-19" class="reference"><a href="#cite_note-19"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup> </td> <td>Ambient </td> <td align="right">1.60×10<sup>3</sup><br />...8.00×10<sup>3</sup> </td> <td align="right">158–172 </td></tr> <tr> <td>9-inch (23 cm) party balloon inflated to rupture<sup id="cite_ref-balloonpoploudness_20-0" class="reference"><a href="#cite_note-balloonpoploudness-20"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> </td> <td>At ear </td> <td align="right">4.92×10<sup>3</sup> </td> <td align="right">168 </td></tr> <tr> <td>9-inch (23 cm) diameter balloon crushed to rupture<sup id="cite_ref-balloonpoploudness_20-1" class="reference"><a href="#cite_note-balloonpoploudness-20"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> </td> <td>At ear </td> <td align="right">1.79×10<sup>3</sup> </td> <td align="right">159 </td></tr> <tr> <td>9-inch (23 cm) party balloon inflated to rupture<sup id="cite_ref-balloonpoploudness_20-2" class="reference"><a href="#cite_note-balloonpoploudness-20"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> </td> <td>0.5 m </td> <td align="right">1.42×10<sup>3</sup> </td> <td align="right">157 </td></tr> <tr> <td>9-inch (23 cm) diameter balloon popped with a pin<sup id="cite_ref-balloonpoploudness_20-3" class="reference"><a href="#cite_note-balloonpoploudness-20"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> </td> <td>At ear </td> <td align="right">1.13×10<sup>3</sup> </td> <td align="right">155 </td></tr> <tr> <td>LRAD 1000Xi <a href="/wiki/Long_Range_Acoustic_Device" class="mw-redirect" title="Long Range Acoustic Device">Long Range Acoustic Device</a><sup id="cite_ref-lradproductsoverview_21-0" class="reference"><a href="#cite_note-lradproductsoverview-21"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup> </td> <td>1 m </td> <td align="right">8.93×10<sup>2</sup> </td> <td align="right">153 </td></tr> <tr> <td>9-inch (23 cm) party balloon inflated to rupture<sup id="cite_ref-balloonpoploudness_20-4" class="reference"><a href="#cite_note-balloonpoploudness-20"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> </td> <td>1 m </td> <td align="right">731 </td> <td align="right">151 </td></tr> <tr> <td><a href="/wiki/Jet_engine" title="Jet engine">Jet engine</a><sup id="cite_ref-Audio1_13-3" class="reference"><a href="#cite_note-Audio1-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> </td> <td>1 m </td> <td align="right">632 </td> <td align="right">150 </td></tr> <tr> <td>9-inch (23 cm) diameter balloon crushed to rupture<sup id="cite_ref-balloonpoploudness_20-5" class="reference"><a href="#cite_note-balloonpoploudness-20"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> </td> <td>0.95 m </td> <td align="right">448 </td> <td align="right">147 </td></tr> <tr> <td>9-inch (23 cm) diameter balloon popped with a pin<sup id="cite_ref-balloonpoploudness_20-6" class="reference"><a href="#cite_note-balloonpoploudness-20"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup> </td> <td>1 m </td> <td align="right">282.5 </td> <td align="right">143 </td></tr> <tr> <td>Loudest <a href="/wiki/Human_voice" title="Human voice">human voice</a><sup id="cite_ref-Shure_22-0" class="reference"><a href="#cite_note-Shure-22"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> </td> <td>1 inch </td> <td align="right">110 </td> <td align="right">135 </td></tr> <tr> <td><a href="/wiki/Trumpet" title="Trumpet">Trumpet</a><sup id="cite_ref-23" class="reference"><a href="#cite_note-23"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> </td> <td>0.5 m </td> <td align="right">63.2 </td> <td align="right">130 </td></tr> <tr> <td><a href="/wiki/Vuvuzela" title="Vuvuzela">Vuvuzela</a> horn<sup id="cite_ref-24" class="reference"><a href="#cite_note-24"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup> </td> <td>1 m </td> <td align="right">20.0 </td> <td align="right">120 </td></tr> <tr> <td><a href="/wiki/Threshold_of_pain" title="Threshold of pain">Threshold of pain</a><sup id="cite_ref-painthres_25-0" class="reference"><a href="#cite_note-painthres-25"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-dictionary_26-0" class="reference"><a href="#cite_note-dictionary-26"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Shure_22-1" class="reference"><a href="#cite_note-Shure-22"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup> </td> <td>At ear </td> <td align="right">20–200 </td> <td align="right">120–140 </td></tr> <tr> <td>Risk of instantaneous <a href="/wiki/Noise-induced_hearing_loss" title="Noise-induced hearing loss">noise-induced hearing loss</a> </td> <td>At ear </td> <td align="right">20.0 </td> <td align="right">120 </td></tr> <tr> <td><a href="/wiki/Jet_engine" title="Jet engine">Jet engine</a> </td> <td>100–30 m </td> <td align="right">6.32–200 </td> <td align="right">110–140 </td></tr> <tr> <td><a href="/wiki/Two-stroke" class="mw-redirect" title="Two-stroke">Two-stroke</a> <a href="/wiki/Chainsaw" title="Chainsaw">chainsaw</a><sup id="cite_ref-sengpielaudio_27-0" class="reference"><a href="#cite_note-sengpielaudio-27"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup> </td> <td>1 m </td> <td align="right">6.32 </td> <td align="right">110 </td></tr> <tr> <td><a href="/wiki/Jackhammer" title="Jackhammer">Jackhammer</a> </td> <td>1 m </td> <td align="right">2.00 </td> <td align="right">100 </td></tr> <tr> <td>Traffic on a busy roadway (combustion engines) </td> <td>10 m </td> <td align="right">0.20–0.63 </td> <td align="right">80–90 </td></tr> <tr> <td><a href="/wiki/Hearing_damage" class="mw-redirect" title="Hearing damage">Hearing damage</a> (over long-term exposure, need not be continuous)<sup id="cite_ref-Hamby_28-0" class="reference"><a href="#cite_note-Hamby-28"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup> </td> <td>At ear </td> <td align="right">0.36 </td> <td align="right">85 </td></tr> <tr> <td><a href="/wiki/Automobile" class="mw-redirect" title="Automobile">Passenger car</a> (combustion engine) </td> <td>10 m </td> <td align="right">0.02–0.20 </td> <td align="right">60–80 </td></tr> <tr> <td>Traffic on a busy roadway (<a href="/wiki/Battery_electric_vehicles" class="mw-redirect" title="Battery electric vehicles">electric vehicles</a>) <sup id="cite_ref-29" class="reference"><a href="#cite_note-29"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup> </td> <td>10 m </td> <td align="right">0.20–0.63 </td> <td align="right">65-75 </td></tr> <tr> <td><a href="/wiki/United_States_Environmental_Protection_Agency" title="United States Environmental Protection Agency">EPA</a>-identified maximum to protect against hearing loss and other disruptive effects from noise, such as sleep disturbance, stress, learning detriment, etc.<sup id="cite_ref-30" class="reference"><a href="#cite_note-30"><span class="cite-bracket">[</span>29<span class="cite-bracket">]</span></a></sup> </td> <td>Ambient </td> <td align="right">0.06 </td> <td align="right">70 </td></tr> <tr> <td>TV (set at home level) </td> <td>1 m </td> <td align="right">0.02 </td> <td align="right">60 </td></tr> <tr> <td>Normal conversation </td> <td>1 m </td> <td align="right">2×10<sup>−3</sup>–0.02 </td> <td align="right">40–60 </td></tr> <tr> <td>Passenger car (electric) <sup id="cite_ref-31" class="reference"><a href="#cite_note-31"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup> </td> <td>10 m </td> <td align="right">0.02–0.20 </td> <td align="right">38-48 </td></tr> <tr> <td>Very calm room </td> <td>Ambient </td> <td align="right">2.00×10<sup>−4</sup><br />...6.32×10<sup>−4</sup> </td> <td align="right">20–30 </td></tr> <tr> <td>Light leaf rustling, calm breathing<sup id="cite_ref-Audio1_13-4" class="reference"><a href="#cite_note-Audio1-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> </td> <td>Ambient </td> <td align="right">6.32×10<sup>−5</sup> </td> <td align="right">10 </td></tr> <tr> <td><a href="/wiki/Auditory_threshold" class="mw-redirect" title="Auditory threshold">Auditory threshold</a> at 1 kHz<sup id="cite_ref-Hamby_28-1" class="reference"><a href="#cite_note-Hamby-28"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup> </td> <td>At ear </td> <td align="right">2.00×10<sup>−5</sup> </td> <td align="right">0 </td></tr> <tr> <td><a href="/wiki/Anechoic_chamber" title="Anechoic chamber">Anechoic chamber</a>, Orfield Labs, <a href="/wiki/A-weighted" class="mw-redirect" title="A-weighted">A-weighted</a><sup id="cite_ref-32" class="reference"><a href="#cite_note-32"><span class="cite-bracket">[</span>31<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-33" class="reference"><a href="#cite_note-33"><span class="cite-bracket">[</span>32<span class="cite-bracket">]</span></a></sup> </td> <td>Ambient </td> <td align="right">6.80×10<sup>−6</sup> </td> <td align="right">−9.4 </td></tr> <tr> <td><a href="/wiki/Anechoic_chamber" title="Anechoic chamber">Anechoic chamber</a>, <a href="/wiki/University_of_Salford" title="University of Salford">University of Salford</a>, <a href="/wiki/A-weighted" class="mw-redirect" title="A-weighted">A-weighted</a><sup id="cite_ref-34" class="reference"><a href="#cite_note-34"><span class="cite-bracket">[</span>33<span class="cite-bracket">]</span></a></sup> </td> <td>Ambient </td> <td align="right">4.80×10<sup>−6</sup> </td> <td align="right">−12.4 </td></tr> <tr> <td><a href="/wiki/Anechoic_chamber" title="Anechoic chamber">Anechoic chamber</a>, Microsoft, <a href="/wiki/A-weighted" class="mw-redirect" title="A-weighted">A-weighted</a><sup id="cite_ref-35" class="reference"><a href="#cite_note-35"><span class="cite-bracket">[</span>34<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-36" class="reference"><a href="#cite_note-36"><span class="cite-bracket">[</span>35<span class="cite-bracket">]</span></a></sup> </td> <td>Ambient </td> <td align="right">1.90×10<sup>−6</sup> </td> <td align="right">−20.35 </td></tr></tbody></table> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist reflist-lower-alpha"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-14">^</a></b></span> <span class="reference-text">All values listed are the effective sound pressure unless otherwise stated.</span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Sound_pressure&action=edit&section=12" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Acoustics" title="Acoustics">Acoustics</a> – Branch of physics involving mechanical waves</li> <li><a href="/wiki/Phon" title="Phon">Phon</a> – Logarithmic unit of loudness level</li> <li><a href="/wiki/Loudness" title="Loudness">Loudness</a> – Subjective perception of sound pressure</li> <li><a href="/wiki/Sone" title="Sone">Sone</a> – Unit of perceived loudness</li> <li><a href="/wiki/Sound_level_meter" title="Sound level meter">Sound level meter</a> – Device for acoustic measurements</li> <li><a href="/wiki/Stevens%27s_power_law" title="Stevens's power law">Stevens's power law</a> – Empirical relationship between actual and perceived changed intensity of stimulus</li> <li><a href="/wiki/Weber%E2%80%93Fechner_law" title="Weber–Fechner law">Weber–Fechner law</a> – Related laws in the field of psychophysics</li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Sound_pressure&action=edit&section=13" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239543626"><div class="reflist"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.engineeringtoolbox.com/sound-pressure-d_711.html">"Sound Pressure Is the Force of Sound on a Surface Area Perpendicular to the Direction of the Sound"</a><span class="reference-accessdate">. Retrieved <span class="nowrap">22 April</span> 2015</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Sound+Pressure+Is+the+Force+of+Sound+on+a+Surface+Area+Perpendicular+to+the+Direction+of+the+Sound&rft_id=http%3A%2F%2Fwww.engineeringtoolbox.com%2Fsound-pressure-d_711.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASound+pressure" class="Z3988"></span></span> </li> <li id="cite_note-Wolfe-2"><span class="mw-cite-backlink">^ <a href="#cite_ref-Wolfe_2-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Wolfe_2-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWolfe" class="citation web cs1">Wolfe, J. <a rel="nofollow" class="external text" href="http://www.phys.unsw.edu.au/jw/z.html">"What is acoustic impedance and why is it important?"</a>. University of New South Wales, Dept. of Physics, Music Acoustics<span class="reference-accessdate">. Retrieved <span class="nowrap">1 January</span> 2014</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=What+is+acoustic+impedance+and+why+is+it+important%3F&rft.pub=University+of+New+South+Wales%2C+Dept.+of+Physics%2C+Music+Acoustics&rft.aulast=Wolfe&rft.aufirst=J.&rft_id=http%3A%2F%2Fwww.phys.unsw.edu.au%2Fjw%2Fz.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASound+pressure" class="Z3988"></span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLonghurst1967" class="citation book cs1">Longhurst, R. S. (1967). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/geometricalphysi0000long"><i>Geometrical and Physical Optics</i></a></span>. Norwich: Longmans.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Geometrical+and+Physical+Optics&rft.place=Norwich&rft.pub=Longmans&rft.date=1967&rft.aulast=Longhurst&rft.aufirst=R.+S.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fgeometricalphysi0000long&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASound+pressure" class="Z3988"></span></span> </li> <li id="cite_note-IEC60027-3-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-IEC60027-3_4-0">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://webstore.iec.ch/webstore/webstore.nsf/artnum/028981">"Letter symbols to be used in electrical technology – Part 3: Logarithmic and related quantities, and their units"</a>, <i>IEC 60027-3 Ed. 3.0</i>, International Electrotechnical Commission, 19 July 2002.</span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAttenboroughPostema2008" class="citation book cs1">Attenborough K, Postema M (2008). <a rel="nofollow" class="external text" href="https://hal.archives-ouvertes.fr/hal-03188302/document"><i>A Pocket-Sized Introduction to Acoustics</i></a>. Kingston upon Hull: The University of Hull. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.5281%2Fzenodo.7504060">10.5281/zenodo.7504060</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-90-812588-2-1" title="Special:BookSources/978-90-812588-2-1"><bdi>978-90-812588-2-1</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=A+Pocket-Sized+Introduction+to+Acoustics&rft.place=Kingston+upon+Hull&rft.pub=The+University+of+Hull&rft.date=2008&rft_id=info%3Adoi%2F10.5281%2Fzenodo.7504060&rft.isbn=978-90-812588-2-1&rft.aulast=Attenborough&rft.aufirst=K&rft.au=Postema%2C+M&rft_id=https%3A%2F%2Fhal.archives-ouvertes.fr%2Fhal-03188302%2Fdocument&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASound+pressure" class="Z3988"></span></span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBiesHansen2003" class="citation book cs1">Bies, David A.; Hansen, Colin (2003). <i>Engineering Noise Control</i>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Engineering+Noise+Control&rft.date=2003&rft.aulast=Bies&rft.aufirst=David+A.&rft.au=Hansen%2C+Colin&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASound+pressure" class="Z3988"></span></span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text">Ross Roeser, Michael Valente, <i>Audiology: Diagnosis</i> (Thieme 2007), p. 240.</span> </li> <li id="cite_note-NIST2008-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-NIST2008_8-0">^</a></b></span> <span class="reference-text">Thompson, A. and Taylor, B. N. Sec. 8.7: "Logarithmic quantities and units: level, neper, bel", <i>Guide for the Use of the International System of Units (SI) 2008 Edition</i>, NIST Special Publication 811, 2nd printing (November 2008), SP811 <a rel="nofollow" class="external text" href="http://physics.nist.gov/cuu/pdf/sp811.pdf">PDF</a>.</span> </li> <li id="cite_note-Morfey-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-Morfey_9-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMorfey2001" class="citation book cs1">Morfey, Christopher L. (2001). <i>Dictionary of Acoustics</i>. San Diego: Academic Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0125069403" title="Special:BookSources/978-0125069403"><bdi>978-0125069403</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Dictionary+of+Acoustics&rft.place=San+Diego&rft.pub=Academic+Press&rft.date=2001&rft.isbn=978-0125069403&rft.aulast=Morfey&rft.aufirst=Christopher+L.&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASound+pressure" class="Z3988"></span></span> </li> <li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.memtechacoustical.com/noise-terms-glossary">"Noise Terms Glossary"</a><span class="reference-accessdate">. Retrieved <span class="nowrap">2012-10-14</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Noise+Terms+Glossary&rft_id=http%3A%2F%2Fwww.memtechacoustical.com%2Fnoise-terms-glossary&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASound+pressure" class="Z3988"></span></span> </li> <li id="cite_note-:0-11"><span class="mw-cite-backlink">^ <a href="#cite_ref-:0_11-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:0_11-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSelf2020" class="citation book cs1">Self, Douglas (2020-04-17). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=L2PdDwAAQBAJ&dq=194+dB+SPL&pg=PP36"><i>Small Signal Audio Design</i></a>. CRC Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-000-05044-8" title="Special:BookSources/978-1-000-05044-8"><bdi>978-1-000-05044-8</bdi></a>. <q>this limit is reached when the rarefaction creates a vacuum, because you can't have a lower pressure than that. This corresponds to about +194 dB SPL.</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Small+Signal+Audio+Design&rft.pub=CRC+Press&rft.date=2020-04-17&rft.isbn=978-1-000-05044-8&rft.aulast=Self&rft.aufirst=Douglas&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DL2PdDwAAQBAJ%26dq%3D194%2BdB%2BSPL%26pg%3DPP36&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASound+pressure" class="Z3988"></span></span> </li> <li id="cite_note-:1-12"><span class="mw-cite-backlink">^ <a href="#cite_ref-:1_12-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:1_12-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGuignardKingNorth_Atlantic_Treaty_Organization_Advisory_Group_for_Aerospace_Research_and_Development_Aerospace_Medical_Panel1972" class="citation book cs1">Guignard, J. C.; King, P.F.; North Atlantic Treaty Organization Advisory Group for Aerospace Research and Development Aerospace Medical Panel (1972). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=LvRJAQAAIAAJ&q=191+dB+SPL"><i>Aeromedical Aspects of Vibration and Noise</i></a>. North Atlantic Treaty Organization, Advisory Group for Aerospace Research and Development. <q>In air at an assumed atmospheric pressure of 1 bar (100,000 N/m<sup>2</sup>) this occurs theoretically at approximately 191 dB SPL (working with rms values</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Aeromedical+Aspects+of+Vibration+and+Noise&rft.pub=North+Atlantic+Treaty+Organization%2C+Advisory+Group+for+Aerospace+Research+and+Development&rft.date=1972&rft.aulast=Guignard&rft.aufirst=J.+C.&rft.au=King%2C+P.F.&rft.au=North+Atlantic+Treaty+Organization+Advisory+Group+for+Aerospace+Research+and+Development+Aerospace+Medical+Panel&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DLvRJAQAAIAAJ%26q%3D191%2BdB%2BSPL&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASound+pressure" class="Z3988"></span></span> </li> <li id="cite_note-Audio1-13"><span class="mw-cite-backlink">^ <a href="#cite_ref-Audio1_13-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Audio1_13-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-Audio1_13-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-Audio1_13-3"><sup><i><b>d</b></i></sup></a> <a href="#cite_ref-Audio1_13-4"><sup><i><b>e</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWiner2013" class="citation book cs1">Winer, Ethan (2013). 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New York and London: Focal Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-240-82100-9" title="Special:BookSources/978-0-240-82100-9"><bdi>978-0-240-82100-9</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=bookitem&rft.atitle=1&rft.btitle=The+Audio+Expert&rft.place=New+York+and+London&rft.pub=Focal+Press&rft.date=2013&rft.isbn=978-0-240-82100-9&rft.aulast=Winer&rft.aufirst=Ethan&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASound+pressure" class="Z3988"></span></span> </li> <li id="cite_note-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-15">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHATAZAWASUGITAOGAWASEO2004" class="citation journal cs1">HATAZAWA, Masayasu; SUGITA, Hiroshi; OGAWA, Takahiro; SEO, Yoshitoki (2004-01-01). <a rel="nofollow" class="external text" href="http://ci.nii.ac.jp/naid/130004080803/">"Performance of a Thermoacoustic Sound Wave Generator driven with Waste Heat of Automobile Gasoline Engine"</a>. <i>Transactions of the Japan Society of Mechanical Engineers B</i>. <b>70</b> (689): <span class="nowrap">292–</span>299. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1299%2Fkikaib.70.292">10.1299/kikaib.70.292</a></span>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/issn/0387-5016">0387-5016</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Transactions+of+the+Japan+Society+of+Mechanical+Engineers+B&rft.atitle=Performance+of+a+Thermoacoustic+Sound+Wave+Generator+driven+with+Waste+Heat+of+Automobile+Gasoline+Engine&rft.volume=70&rft.issue=689&rft.pages=%3Cspan+class%3D%22nowrap%22%3E292-%3C%2Fspan%3E299&rft.date=2004-01-01&rft_id=info%3Adoi%2F10.1299%2Fkikaib.70.292&rft.issn=0387-5016&rft.aulast=HATAZAWA&rft.aufirst=Masayasu&rft.au=SUGITA%2C+Hiroshi&rft.au=OGAWA%2C+Takahiro&rft.au=SEO%2C+Yoshitoki&rft_id=http%3A%2F%2Fci.nii.ac.jp%2Fnaid%2F130004080803%2F&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASound+pressure" class="Z3988"></span></span> </li> <li id="cite_note-16"><span class="mw-cite-backlink"><b><a href="#cite_ref-16">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.bksv.com/en/knowledge/blog/perspectives/krakatoa-eruption-sound">"Krakatoa Eruption – The Loudest Sound"</a>. <i>Brüel & Kjær</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2021-03-24</span></span>. <q>160 km (99 miles) away from the source, registered a sound pressure level spike of more than 2½ inches of mercury (8.5 kPa), equivalent to 172 decibels.</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Br%C3%BCel+%26+Kj%C3%A6r&rft.atitle=Krakatoa+Eruption+%E2%80%93+The+Loudest+Sound&rft_id=https%3A%2F%2Fwww.bksv.com%2Fen%2Fknowledge%2Fblog%2Fperspectives%2Fkrakatoa-eruption-sound&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASound+pressure" class="Z3988"></span></span> </li> <li id="cite_note-winchester-17"><span class="mw-cite-backlink"><b><a href="#cite_ref-winchester_17-0">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWinchester2003" class="citation book cs1"><a href="/wiki/Simon_Winchester" title="Simon Winchester">Winchester, Simon</a> (2003). <a href="/wiki/Krakatoa:_The_Day_the_World_Exploded" title="Krakatoa: The Day the World Exploded"><i>Krakatoa: The Day the World Exploded, August 27, 1883</i></a>. 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Retrieved <span class="nowrap">5 Mar</span> 2012</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=sengpielaudio&rft.atitle=Decibel+Table+%E2%80%93+SPL+%E2%80%93+Loudness+Comparison+Chart&rft_id=http%3A%2F%2Fwww.sengpielaudio.com%2FTableOfSoundPressureLevels.htm&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASound+pressure" class="Z3988"></span></span> </li> <li id="cite_note-Hamby-28"><span class="mw-cite-backlink">^ <a href="#cite_ref-Hamby_28-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Hamby_28-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHamby" class="citation web cs1">Hamby, William. <a rel="nofollow" class="external text" href="http://www.makeitlouder.com/Decibel%20Level%20Chart.txt">"Ultimate Sound Pressure Level Decibel Table"</a>. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20051019001826/http://www.makeitlouder.com/Decibel%20Level%20Chart.txt">Archived</a> from the original on 2005-10-19.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Ultimate+Sound+Pressure+Level+Decibel+Table&rft.aulast=Hamby&rft.aufirst=William&rft_id=http%3A%2F%2Fwww.makeitlouder.com%2FDecibel%2520Level%2520Chart.txt&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASound+pressure" class="Z3988"></span></span> </li> <li id="cite_note-29"><span class="mw-cite-backlink"><b><a href="#cite_ref-29">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNicolas_Misdariis,_Louis-Ferdinand_Pardo2017" class="citation cs2">Nicolas Misdariis, Louis-Ferdinand Pardo (Aug 2017), <a rel="nofollow" class="external text" href="https://hal.science/hal-01708883"><i>The sound of silence of electric vehicles – Issues and answers</i></a>, InterNoise, HAL Open Science, Hong-Kong, China<span class="reference-accessdate">, retrieved <span class="nowrap">May 2,</span> 2024</span></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+sound+of+silence+of+electric+vehicles+%E2%80%93+Issues+and+answers&rft.pub=InterNoise%2C+HAL+Open+Science%2C+Hong-Kong%2C+China&rft.date=2017-08&rft.au=Nicolas+Misdariis%2C+Louis-Ferdinand+Pardo&rft_id=https%3A%2F%2Fhal.science%2Fhal-01708883&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASound+pressure" class="Z3988"></span></span> </li> <li id="cite_note-30"><span class="mw-cite-backlink"><b><a href="#cite_ref-30">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation pressrelease cs1"><a rel="nofollow" class="external text" href="https://archive.epa.gov/epa/aboutepa/epa-identifies-noise-levels-affecting-health-and-welfare.html">"EPA Identifies Noise Levels Affecting Health and Welfare"</a> (Press release). <a href="/wiki/United_States_Environmental_Protection_Agency" title="United States Environmental Protection Agency">Environmental Protection Agency</a>. April 2, 1974<span class="reference-accessdate">. Retrieved <span class="nowrap">March 27,</span> 2017</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=EPA+Identifies+Noise+Levels+Affecting+Health+and+Welfare&rft.pub=Environmental+Protection+Agency&rft.date=1974-04-02&rft_id=https%3A%2F%2Farchive.epa.gov%2Fepa%2Faboutepa%2Fepa-identifies-noise-levels-affecting-health-and-welfare.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASound+pressure" class="Z3988"></span></span> </li> <li id="cite_note-31"><span class="mw-cite-backlink"><b><a href="#cite_ref-31">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFNicolas_Misdariis,_Louis-Ferdinand_Pardo2017" class="citation web cs1">Nicolas Misdariis, Louis-Ferdinand Pardo (Aug 2017). <a rel="nofollow" class="external text" href="https://hal.science/hal-01708883">"The sound of silence of electric vehicles – Issues and answers"</a>. InterNoise, HAL Open Science, Hong-Kong, China<span class="reference-accessdate">. Retrieved <span class="nowrap">May 2,</span> 2024</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=The+sound+of+silence+of+electric+vehicles+%E2%80%93+Issues+and+answers&rft.pub=InterNoise%2C+HAL+Open+Science%2C+Hong-Kong%2C+China&rft.date=2017-08&rft.au=Nicolas+Misdariis%2C+Louis-Ferdinand+Pardo&rft_id=https%3A%2F%2Fhal.science%2Fhal-01708883&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASound+pressure" class="Z3988"></span></span> </li> <li id="cite_note-32"><span class="mw-cite-backlink"><b><a href="#cite_ref-32">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.orfieldlabs.com/pdfs/chamber.pdf">"<span class="cs1-kern-left"></span>'The Quietest Place on Earth' – Guinness World Records Certificate, 2005"</a> <span class="cs1-format">(PDF)</span>. Orfield Labs.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=%27The+Quietest+Place+on+Earth%27+%E2%80%93+Guinness+World+Records+Certificate%2C+2005&rft.pub=Orfield+Labs&rft_id=http%3A%2F%2Fwww.orfieldlabs.com%2Fpdfs%2Fchamber.pdf&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASound+pressure" class="Z3988"></span></span> </li> <li id="cite_note-33"><span class="mw-cite-backlink"><b><a href="#cite_ref-33">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMiddlemiss2007" class="citation web cs1">Middlemiss, Neil (December 18, 2007). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20101121101851/http://www.audiojunkies.com/blog/902/the-quietest-place-on-earth-orfield-labs">"The Quietest Place on Earth – Orfield Labs"</a>. <i>Audio Junkies</i>. Archived from <a rel="nofollow" class="external text" href="http://www.audiojunkies.com/blog/902/the-quietest-place-on-earth-orfield-labs">the original</a> on 2010-11-21.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Audio+Junkies&rft.atitle=The+Quietest+Place+on+Earth+%E2%80%93+Orfield+Labs&rft.date=2007-12-18&rft.aulast=Middlemiss&rft.aufirst=Neil&rft_id=http%3A%2F%2Fwww.audiojunkies.com%2Fblog%2F902%2Fthe-quietest-place-on-earth-orfield-labs&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASound+pressure" class="Z3988"></span></span> </li> <li id="cite_note-34"><span class="mw-cite-backlink"><b><a href="#cite_ref-34">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFEustace" class="citation web cs1">Eustace, Dave. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20190304052554/http://www.acoustics.salford.ac.uk/facilities/?content=anechoic">"Anechoic Chamber"</a>. University of Salford. Archived from <a rel="nofollow" class="external text" href="http://www.acoustics.salford.ac.uk/facilities/?content=anechoic">the original</a> on 2019-03-04.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Anechoic+Chamber&rft.pub=University+of+Salford&rft.aulast=Eustace&rft.aufirst=Dave&rft_id=http%3A%2F%2Fwww.acoustics.salford.ac.uk%2Ffacilities%2F%3Fcontent%3Danechoic&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASound+pressure" class="Z3988"></span></span> </li> <li id="cite_note-35"><span class="mw-cite-backlink"><b><a href="#cite_ref-35">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.guinnessworldrecords.com/news/2015/10/microsoft-lab-sets-new-record-for-the-worlds-quietest-place-399444">"Microsoft Lab Sets New Record for the World's Quietest Place"</a>. 2015-10-02<span class="reference-accessdate">. Retrieved <span class="nowrap">2016-09-20</span></span>. <q>The computer company has built an anechoic chamber in which highly sensitive tests reported an average background noise reading of an unimaginably quiet −20.35 dBA (decibels A-weighted).</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Microsoft+Lab+Sets+New+Record+for+the+World%27s+Quietest+Place&rft.date=2015-10-02&rft_id=http%3A%2F%2Fwww.guinnessworldrecords.com%2Fnews%2F2015%2F10%2Fmicrosoft-lab-sets-new-record-for-the-worlds-quietest-place-399444&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASound+pressure" class="Z3988"></span></span> </li> <li id="cite_note-36"><span class="mw-cite-backlink"><b><a href="#cite_ref-36">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://news.microsoft.com/stories/building87/audio-lab.php">"Check Out the World's Quietest Room"</a>. <i>Microsoft: Inside B87</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2016-09-20</span></span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Microsoft%3A+Inside+B87&rft.atitle=Check+Out+the+World%27s+Quietest+Room&rft_id=http%3A%2F%2Fnews.microsoft.com%2Fstories%2Fbuilding87%2Faudio-lab.php&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASound+pressure" class="Z3988"></span></span> </li> </ol></div></div> <dl><dt>General</dt></dl> <ul><li>Beranek, Leo L., <i>Acoustics</i> (1993), Acoustical Society of America, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-88318-494-X" title="Special:BookSources/0-88318-494-X">0-88318-494-X</a>.</li> <li>Daniel R. Raichel, <i>The Science and Applications of Acoustics</i> (2006), Springer New York, <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/1441920803" title="Special:BookSources/1441920803">1441920803</a>.</li></ul> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Sound_pressure&action=edit&section=14" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Commons-logo.svg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/12px-Commons-logo.svg.png" decoding="async" width="12" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/18px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/24px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></a></span> Media related to <a href="https://commons.wikimedia.org/wiki/Category:Sound_pressure" class="extiw" title="commons:Category:Sound pressure">Sound pressure</a> at Wikimedia Commons</li> <li><a rel="nofollow" class="external text" href="http://www.usmotors.com/products/ProFacts/sound_power_and_sound_pressure.htm">Sound Pressure and Sound Power, Two Commonly Confused Characteristics of Sound</a></li> <li><a rel="nofollow" class="external text" href="http://www.gcaudio.com/resources/howtos/loudness.html">Decibel (Loudness) Comparison Chart</a></li></ul> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1236075235">.mw-parser-output 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magnitude (frequency)">Frequency</a></li> <li><a href="/wiki/Orders_of_magnitude_(illuminance)" title="Orders of magnitude (illuminance)">Illuminance</a></li> <li><a href="/wiki/Orders_of_magnitude_(length)" title="Orders of magnitude (length)">Length</a></li> <li><a href="/wiki/Orders_of_magnitude_(luminance)" class="mw-redirect" title="Orders of magnitude (luminance)">Luminance</a></li> <li><a href="/wiki/Orders_of_magnitude_(magnetic_moment)" title="Orders of magnitude (magnetic moment)">Magnetic moment</a></li> <li><a href="/wiki/Orders_of_magnitude_(magnetic_field)" title="Orders of magnitude (magnetic field)">Magnetic field</a></li> <li><a href="/wiki/Orders_of_magnitude_(mass)" title="Orders of magnitude (mass)">Mass</a></li> <li><a href="/wiki/Orders_of_magnitude_(molar_concentration)" title="Orders of magnitude (molar concentration)">Molarity</a></li> <li><a href="/wiki/Orders_of_magnitude_(numbers)" title="Orders of magnitude (numbers)">Numbers</a></li> <li><a href="/wiki/Orders_of_magnitude_(power)" title="Orders of magnitude (power)">Power</a></li> <li><a href="/wiki/Orders_of_magnitude_(pressure)" title="Orders of magnitude (pressure)">Pressure</a></li> <li><a href="/wiki/Orders_of_magnitude_(probability)" title="Orders of magnitude (probability)">Probability</a></li> <li><a href="/wiki/Orders_of_magnitude_(radiation)" title="Orders of magnitude (radiation)">Radiation</a></li> <li><a class="mw-selflink-fragment" href="#Examples_of_sound_pressure">Sound pressure</a></li> <li><a href="/wiki/Orders_of_magnitude_(specific_heat_capacity)" title="Orders of magnitude (specific heat capacity)">Specific heat capacity</a></li> <li><a href="/wiki/Orders_of_magnitude_(speed)" title="Orders of magnitude (speed)">Speed</a></li> <li><a href="/wiki/Orders_of_magnitude_(temperature)" title="Orders of magnitude (temperature)">Temperature</a></li> <li><a href="/wiki/Orders_of_magnitude_(torque)" title="Orders of magnitude (torque)">Torque</a></li> <li><a href="/wiki/Orders_of_magnitude_(time)" title="Orders of magnitude (time)">Time</a></li> <li><a href="/wiki/Orders_of_magnitude_(voltage)" title="Orders of magnitude (voltage)">Voltage</a></li> <li><a href="/wiki/Orders_of_magnitude_(volume)" title="Orders of magnitude (volume)">Volume</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">See also</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Back-of-the-envelope_calculation" title="Back-of-the-envelope calculation">Back-of-the-envelope calculation</a></li> <li><a href="/wiki/Fermi_problem" title="Fermi problem">Fermi problem</a></li> <li><a href="/wiki/Power_of_10" title="Power of 10">Powers of 10</a> and <a href="/wiki/Decade_(log_scale)" title="Decade (log scale)">decades</a> <ul><li><a href="/wiki/Decimal" title="Decimal">10th</a></li> <li><a href="/wiki/Hundredth" title="Hundredth">100th</a></li> <li><a href="/wiki/Millionth" title="Millionth">1000000th</a></li></ul></li> <li><a href="/wiki/Metric_prefix" title="Metric prefix">Metric (SI) prefix</a></li> <li><a href="/wiki/Macroscopic_scale" title="Macroscopic scale">Macroscopic scale</a></li> <li><a href="/wiki/Microscopic_scale" title="Microscopic scale">Microscopic scale</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Related</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Astronomical_system_of_units" title="Astronomical system of units">Astronomical system of units</a></li> <li><a href="/wiki/Location_of_Earth" title="Location of Earth">Earth's location in the Universe</a></li> <li><i><a href="/wiki/Cosmic_View" title="Cosmic View">Cosmic View</a></i> (1957 book)</li> <li><i><a href="/wiki/To_the_Moon_and_Beyond" title="To the Moon and Beyond">To the Moon and Beyond</a></i> (1964 film)</li> <li><i><a href="/wiki/Cosmic_Zoom" title="Cosmic Zoom">Cosmic Zoom</a></i> (1968 film)</li> <li><a href="/wiki/Powers_of_Ten_(film)" title="Powers of Ten (film)"><i>Powers of Ten</i> (1968 and 1977 films)</a></li> <li><a href="/wiki/Cosmic_Voyage_(1996_film)" title="Cosmic Voyage (1996 film)"><i>Cosmic Voyage</i> (1996 documentary)</a></li> <li><i><a href="/wiki/The_Scale_of_the_Universe" title="The Scale of the Universe">The Scale of the Universe</a></i> (2010)</li> <li><i><a href="/wiki/Cosmic_Eye" title="Cosmic Eye">Cosmic Eye</a></i> (2012)</li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div> <ul><li><span class="noviewer" typeof="mw:File"><span title="Category"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/16px-Symbol_category_class.svg.png" decoding="async" width="16" height="16" class="mw-file-element" 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Sound pressure - Wikipedia