Sound power - Wikipedia

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data-event-name="pinnable-header.vector-toc.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">hide</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">(Top)</div> </a> </li> <li id="toc-Sound_power_level_LWA" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Sound_power_level_LWA"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Sound power level <i>L</i><sub>WA</sub></span> </div> </a> <button aria-controls="toc-Sound_power_level_LWA-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 power level <i>L</i><sub>WA</sub> subsection</span> </button> <ul id="toc-Sound_power_level_LWA-sublist" class="vector-toc-list"> <li id="toc-Table_of_selected_sound_sources" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Table_of_selected_sound_sources"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>Table of selected sound sources</span> </div> </a> <ul id="toc-Table_of_selected_sound_sources-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Mathematical_definition" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Mathematical_definition"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Mathematical definition</span> </div> </a> <ul id="toc-Mathematical_definition-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Relationships_with_other_quantities" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Relationships_with_other_quantities"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Relationships with other quantities</span> </div> </a> <ul id="toc-Relationships_with_other_quantities-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Sound_power_level" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Sound_power_level"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Sound power level</span> </div> </a> <button aria-controls="toc-Sound_power_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 power level subsection</span> </button> <ul id="toc-Sound_power_level-sublist" class="vector-toc-list"> <li id="toc-Relationship_with_sound_pressure_level" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Relationship_with_sound_pressure_level"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1</span> <span>Relationship with sound pressure level</span> </div> </a> <ul id="toc-Relationship_with_sound_pressure_level-sublist" class="vector-toc-list"> </ul> </li> </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">5</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">6</span> <span>External links</span> </div> </a> <ul id="toc-External_links-sublist" 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from <a href="/w/index.php?title=Sound_power_level&redirect=no" class="mw-redirect" title="Sound power level">Sound power level</a>)</span></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Rate at which sound energy is reflected or transmitted per unit time</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 href="/wiki/Sound_pressure" title="Sound pressure">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 class="mw-selflink selflink">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 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li:first-child::before,.mw-parser-output .hlist dt dd:first-child::before,.mw-parser-output .hlist dt dt:first-child::before,.mw-parser-output .hlist dt li:first-child::before,.mw-parser-output .hlist li dd:first-child::before,.mw-parser-output .hlist li dt:first-child::before,.mw-parser-output .hlist li li:first-child::before{content:" (";font-weight:normal}.mw-parser-output .hlist dd dd:last-child::after,.mw-parser-output .hlist dd dt:last-child::after,.mw-parser-output .hlist dd li:last-child::after,.mw-parser-output .hlist dt dd:last-child::after,.mw-parser-output .hlist dt dt:last-child::after,.mw-parser-output .hlist dt li:last-child::after,.mw-parser-output .hlist li dd:last-child::after,.mw-parser-output .hlist li dt:last-child::after,.mw-parser-output .hlist li 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 power</b> or <b>acoustic power</b> is the rate at which <a href="/wiki/Sound_energy" title="Sound energy">sound energy</a> is emitted, <a href="/wiki/Reflected" class="mw-redirect" title="Reflected">reflected</a>, <a href="/wiki/Acoustic_transmission" title="Acoustic transmission">transmitted</a> or received, per unit time.<sup id="cite_ref-clinical_1-0" class="reference"><a href="#cite_note-clinical-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> It is defined<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> as "through a surface, the product of the <a href="/wiki/Sound_pressure" title="Sound pressure">sound pressure</a>, and the component of the <a href="/wiki/Particle_velocity" title="Particle velocity">particle velocity</a>, at a point on the surface in the direction <a href="/wiki/Normal_(geometry)" title="Normal (geometry)">normal</a> to the surface, <a href="/wiki/Surface_integral" title="Surface integral">integrated over</a> that surface." The <a href="/wiki/International_System_of_Units" title="International System of Units">SI unit</a> of sound power is the <a href="/wiki/Watt" title="Watt">watt</a> (W).<sup id="cite_ref-clinical_1-1" class="reference"><a href="#cite_note-clinical-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> It relates to the power of the sound force on a surface enclosing a sound source, in air. </p><p>For a sound source, unlike sound pressure, sound power is neither room-dependent nor distance-dependent. Sound pressure is a property of the field at a point in space, while sound power is a property of a sound source, equal to the total power emitted by that source in all directions. Sound power passing through an area is sometimes called <i>sound <a href="/wiki/Flux" title="Flux">flux</a></i> or <i>acoustic flux</i> through that area. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Sound_power_level_LWA">Sound power level <i>L</i><sub>WA</sub></h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Sound_power&action=edit&section=1" title="Edit section: Sound power level LWA"><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:Atlas_Copco_XAHS_347-pic7-Max._sound_power_level.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/db/Atlas_Copco_XAHS_347-pic7-Max._sound_power_level.jpg/220px-Atlas_Copco_XAHS_347-pic7-Max._sound_power_level.jpg" decoding="async" width="220" height="237" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/db/Atlas_Copco_XAHS_347-pic7-Max._sound_power_level.jpg/330px-Atlas_Copco_XAHS_347-pic7-Max._sound_power_level.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/db/Atlas_Copco_XAHS_347-pic7-Max._sound_power_level.jpg/440px-Atlas_Copco_XAHS_347-pic7-Max._sound_power_level.jpg 2x" data-file-width="691" data-file-height="744" /></a><figcaption>Maximum sound power level (<a href="/wiki/A-weighting" title="A-weighting"><i>L</i><sub>WA</sub></a>) related to a portable <a href="/wiki/Air_compressor" title="Air compressor">air compressor</a></figcaption></figure><p>Regulations often specify a method for measurement<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> that integrates sound pressure over a surface enclosing the source. <i>L</i><sub>WA</sub> specifies the power delivered to that surface in decibels relative to one picowatt. Devices (e.g., a vacuum cleaner) often have labeling requirements and maximum amounts they are allowed to produce. The <a href="/wiki/A-weighting" title="A-weighting">A-weighting</a> scale is used in the calculation as the metric is concerned with the loudness as perceived by the human ear. Measurements<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> in accordance with ISO 3744 are taken at 6 to 12 defined points around the device in a hemi-anechoic space. The test environment can be located indoors or outdoors. The required environment is on hard ground in a large open space or hemi-anechoic chamber (free-field over a reflecting plane.) </p><div class="mw-heading mw-heading3"><h3 id="Table_of_selected_sound_sources">Table of selected sound sources</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Sound_power&action=edit&section=2" title="Edit section: Table of selected sound sources"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Here is a table of some examples, from an on-line source.<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> For omnidirectional point sources in free space, sound power in <i>L</i><sub>wA</sub> is equal to <a href="/wiki/Sound_pressure_level" class="mw-redirect" title="Sound pressure level">sound pressure level</a> in dB above 20 micropascals at a distance of 0.2821 m<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p> <table class="wikitable"> <tbody><tr> <th>Situation and<br />sound source</th> <th>Sound power<br />(<a href="/wiki/Watt" title="Watt">W</a>)</th> <th>Sound power level<br />(<a href="/wiki/Decibel" title="Decibel">dB</a> ref 10<sup>−12</sup> W) </th></tr> <tr> <td><a href="/wiki/Saturn_V" title="Saturn V">Saturn V</a> rocket<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></td> <td align="right"><span class="nowrap"><span data-sort-value="7008100000000000000♠"></span>100<span style="margin-left:.25em;">000</span><span style="margin-left:.25em;">000</span></span></td> <td align="right">200 </td></tr> <tr> <td><a href="/wiki/Turbojet" title="Turbojet">Turbojet</a> engine</td> <td align="right"><span class="nowrap"><span data-sort-value="7005100000000000000♠"></span>100<span style="margin-left:.25em;">000</span></span></td> <td align="right">170 </td></tr> <tr> <td><a href="/wiki/Turbofan" title="Turbofan">Turbofan</a> aircraft at take-off</td> <td align="right"><span class="nowrap"><span data-sort-value="7003100000000000000♠"></span>1000</span></td> <td align="right">150 </td></tr> <tr> <td><a href="/wiki/Turboprop" title="Turboprop">Turboprop</a> aircraft at take-off</td> <td align="right"><span class="nowrap"><span data-sort-value="7002100000000000000♠"></span>100</span></td> <td align="right">140 </td></tr> <tr> <td><a href="/wiki/Machine_gun" title="Machine gun">Machine gun</a> <br />Large <a href="/wiki/Pipe_organ" title="Pipe organ">pipe organ</a></td> <td align="right"><span class="nowrap"><span data-sort-value="7001100000000000000♠"></span>10</span></td> <td align="right">130 </td></tr> <tr> <td><a href="/wiki/Symphony_orchestra" class="mw-redirect" title="Symphony orchestra">Symphony orchestra</a><br />Heavy <a href="/wiki/Thunder" title="Thunder">thunder</a><br /><a href="/wiki/Sonic_boom" title="Sonic boom">Sonic boom</a></td> <td align="right"><span class="nowrap"><span data-sort-value="7000100000000000000♠"></span>1</span></td> <td align="right">120 </td></tr> <tr> <td><a href="/wiki/Rock_concert" title="Rock concert">Rock concert</a> (1970s)<br /><a href="/wiki/Chain_saw" class="mw-redirect" title="Chain saw">Chain saw</a><br />Accelerating <a href="/wiki/Motorcycle" title="Motorcycle">motorcycle</a></td> <td align="right"><span class="nowrap"><span data-sort-value="6999100000000000000♠"></span>0.1</span></td> <td align="right">110 </td></tr> <tr> <td><a href="/wiki/Lawn_mower" title="Lawn mower">Lawn mower</a><br />Car at highway speed<br /><a href="/wiki/Rapid_transit" title="Rapid transit">Subway steel wheels</a></td> <td align="right"><span class="nowrap"><span data-sort-value="6998100000000000000♠"></span>0.01</span></td> <td align="right">100 </td></tr> <tr> <td>Large <a href="/wiki/Diesel_engine" title="Diesel engine">diesel vehicle</a></td> <td align="right"><span class="nowrap"><span data-sort-value="6997100000000000000♠"></span>0.001</span></td> <td align="right">90 </td></tr> <tr> <td>Loud <a href="/wiki/Alarm_clock" title="Alarm clock">alarm clock</a></td> <td align="right"><span class="nowrap"><span data-sort-value="6996100000000000000♠"></span>0.0001</span></td> <td align="right">80 </td></tr> <tr> <td>Relatively quiet <a href="/wiki/Vacuum_cleaner" title="Vacuum cleaner">vacuum cleaner</a></td> <td align="right"><span class="nowrap"><span data-sort-value="6995100000000000000♠"></span>10<sup>−5</sup></span></td> <td align="right">70 </td></tr> <tr> <td><a href="/wiki/Hair_dryer" title="Hair dryer">Hair dryer</a></td> <td align="right"><span class="nowrap"><span data-sort-value="6994100000000000000♠"></span>10<sup>−6</sup></span></td> <td align="right">60 </td></tr> <tr> <td>Radio or TV</td> <td align="right"><span class="nowrap"><span data-sort-value="6993100000000000000♠"></span>10<sup>−7</sup></span></td> <td align="right">50 </td></tr> <tr> <td><a href="/wiki/Refrigerator" title="Refrigerator">Refrigerator</a><br />Low voice</td> <td align="right"><span class="nowrap"><span data-sort-value="6992100000000000000♠"></span>10<sup>−8</sup></span></td> <td align="right">40 </td></tr> <tr> <td>Quiet conversation</td> <td align="right"><span class="nowrap"><span data-sort-value="6991100000000000000♠"></span>10<sup>−9</sup></span></td> <td align="right">30 </td></tr> <tr> <td>Whisper of one person<br />Wristwatch ticking</td> <td align="right"><span class="nowrap"><span data-sort-value="6990100000000000000♠"></span>10<sup>−10</sup></span></td> <td align="right">20 </td></tr> <tr> <td>Human breath of one person</td> <td align="right"><span class="nowrap"><span data-sort-value="6989100000000000000♠"></span>10<sup>−11</sup></span></td> <td align="right">10 </td></tr> <tr> <td>Reference value</td> <td align="right"><span class="nowrap"><span data-sort-value="6988100000000000000♠"></span>10<sup>−12</sup></span></td> <td align="right">0 </td></tr></tbody></table> <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_power&action=edit&section=3" title="Edit section: Mathematical definition"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Sound power, denoted <i>P</i>, is defined by<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P=\mathbf {f} \cdot \mathbf {v} =Ap\,\mathbf {u} \cdot \mathbf {v} =Apv}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">f</mi> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> <mo>=</mo> <mi>A</mi> <mi>p</mi> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">u</mi> </mrow> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">v</mi> </mrow> <mo>=</mo> <mi>A</mi> <mi>p</mi> <mi>v</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P=\mathbf {f} \cdot \mathbf {v} =Ap\,\mathbf {u} \cdot \mathbf {v} =Apv}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/aa19bcbb582c91f0feeb373a3ea8b008154f521c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:27.099ex; height:2.509ex;" alt="{\displaystyle P=\mathbf {f} \cdot \mathbf {v} =Ap\,\mathbf {u} \cdot \mathbf {v} =Apv}"></span></dd></dl> <p>where </p> <ul><li><b>f</b> is the sound force of unit vector <b>u</b>;</li> <li><b>v</b> is the <a href="/wiki/Particle_velocity" title="Particle velocity">particle velocity</a> of projection <i>v</i> along <b>u</b>;</li> <li><i>A</i> is the area;</li> <li><i>p</i> is the <a href="/wiki/Sound_pressure" title="Sound pressure">sound pressure</a>.</li></ul> <p>In a <a href="/wiki/Transmission_medium" title="Transmission medium">medium</a>, the sound power is given by </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P={\frac {Ap^{2}}{\rho c}}\cos \theta ,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>A</mi> <msup> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mrow> <mi>ρ</mi> <mi>c</mi> </mrow> </mfrac> </mrow> <mi>cos</mi> <mo>⁡</mo> <mi>θ</mi> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P={\frac {Ap^{2}}{\rho c}}\cos \theta ,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/36d3b5b1dabf0184defa544249d7edaeee1b5a29" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:15.269ex; height:6.176ex;" alt="{\displaystyle P={\frac {Ap^{2}}{\rho c}}\cos \theta ,}"></span></dd></dl> <p>where </p> <ul><li><i>A</i> is the area of the surface;</li> <li><i>ρ</i> is the <a href="/wiki/Mass_density" class="mw-redirect" title="Mass density">mass density</a>;</li> <li><i>c</i> is the <a href="/wiki/Sound_velocity" class="mw-redirect" title="Sound velocity">sound velocity</a>;</li> <li><i>θ</i> is the angle between the direction of propagation of the sound and the normal to the surface.</li> <li><i>p</i> is the <a href="/wiki/Sound_pressure" title="Sound pressure">sound pressure</a>.</li></ul> <p>For example, a sound at SPL = 85 dB or <i>p</i> = 0.356 Pa in air (<i>ρ</i> = <span class="nowrap"><span data-sort-value="7000120000000000000♠"></span>1.2 kg⋅m<sup>−3</sup></span> and <i>c</i> = <span class="nowrap"><span data-sort-value="7002343000000000000♠"></span>343 m⋅s<sup>−1</sup></span>) through a surface of area <i>A</i> = <span class="nowrap"><span data-sort-value="7000100000000000000♠"></span>1 m<sup>2</sup></span> normal to the direction of propagation (<i>θ</i> = 0°) has a sound energy flux <i>P</i> = <span class="nowrap"><span data-sort-value="6996300000000000000♠"></span>0.3 mW</span>. </p><p>This is the parameter one would be interested in when converting noise back into usable energy, along with any losses in the capturing device. </p> <div class="mw-heading mw-heading2"><h2 id="Relationships_with_other_quantities">Relationships with other quantities</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Sound_power&action=edit&section=4" title="Edit section: Relationships with other quantities"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Sound power is related to <a href="/wiki/Sound_intensity" title="Sound intensity">sound intensity</a>: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P=AI,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> <mo>=</mo> <mi>A</mi> <mi>I</mi> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P=AI,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/abad01c93113e2e092c9bd0a5aa079df1b9b10c2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.406ex; height:2.509ex;" alt="{\displaystyle P=AI,}"></span></dd></dl> <p>where </p> <ul><li><i>A</i> stands for the area;</li> <li><i>I</i> stands for the sound intensity.</li></ul> <p>Sound power is related <a href="/wiki/Sound_energy_density" title="Sound energy density">sound energy density</a>: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P=Acw,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> <mo>=</mo> <mi>A</mi> <mi>c</mi> <mi>w</mi> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P=Acw,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3a6420bd46f5e538a39a796de264d7bada314ffd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:9.905ex; height:2.509ex;" alt="{\displaystyle P=Acw,}"></span></dd></dl> <p>where </p> <ul><li><i>c</i> stands for the <a href="/wiki/Speed_of_sound" title="Speed of sound">speed of sound</a>;</li> <li><i>w</i> stands for the sound energy density.</li></ul> <div class="mw-heading mw-heading2"><h2 id="Sound_power_level">Sound power level</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Sound_power&action=edit&section=5" title="Edit section: Sound power level"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">For other uses, see <a href="/wiki/Sound_level_(disambiguation)" class="mw-redirect mw-disambig" title="Sound level (disambiguation)">Sound level</a>.</div> <p><b>Sound power level</b> (SWL) or <b>acoustic power level</b> is a <a href="/wiki/Level_(logarithmic_quantity)" title="Level (logarithmic quantity)">logarithmic measure</a> of the power of a sound relative to a reference value.<br /> Sound power level, denoted <i>L</i><sub><i>W</i></sub> and measured in <a href="/wiki/Decibel" title="Decibel">dB</a>,<sup id="cite_ref-IEC60027-3_9-0" class="reference"><a href="#cite_note-IEC60027-3-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> is defined by:<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> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle L_{W}={\frac {1}{2}}\ln \!\left({\frac {P}{P_{0}}}\right)\!~\mathrm {Np} =\log _{10}\!\left({\frac {P}{P_{0}}}\right)\!~\mathrm {B} =10\log _{10}\!\left({\frac {P}{P_{0}}}\right)\!~\mathrm {dB} ,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>W</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mi>ln</mi> <mspace width="negativethinmathspace" /> <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> <mspace width="negativethinmathspace" /> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">N</mi> <mi mathvariant="normal">p</mi> </mrow> <mo>=</mo> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>10</mn> </mrow> </msub> <mspace width="negativethinmathspace" /> <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> <mspace width="negativethinmathspace" /> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">B</mi> </mrow> <mo>=</mo> <mn>10</mn> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>10</mn> </mrow> </msub> <mspace width="negativethinmathspace" /> <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> <mspace width="negativethinmathspace" /> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> <mi mathvariant="normal">B</mi> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L_{W}={\frac {1}{2}}\ln \!\left({\frac {P}{P_{0}}}\right)\!~\mathrm {Np} =\log _{10}\!\left({\frac {P}{P_{0}}}\right)\!~\mathrm {B} =10\log _{10}\!\left({\frac {P}{P_{0}}}\right)\!~\mathrm {dB} ,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2ac3532afc128a2a6364427220ca08d9b3708955" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:59.985ex; height:6.176ex;" alt="{\displaystyle L_{W}={\frac {1}{2}}\ln \!\left({\frac {P}{P_{0}}}\right)\!~\mathrm {Np} =\log _{10}\!\left({\frac {P}{P_{0}}}\right)\!~\mathrm {B} =10\log _{10}\!\left({\frac {P}{P_{0}}}\right)\!~\mathrm {dB} ,}"></span></dd></dl> <p>where </p> <ul><li><i>P</i> is the sound power;</li> <li><i>P</i><sub>0</sub> is the <i>reference sound power</i>;</li> <li><span class="nowrap">1 Np = 1</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</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</span> is the <a href="/wiki/Decibel" title="Decibel">decibel</a>.</li></ul> <p>The commonly used reference sound power in air is<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P_{0}=1~\mathrm {pW} .}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>=</mo> <mn>1</mn> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">p</mi> <mi mathvariant="normal">W</mi> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P_{0}=1~\mathrm {pW} .}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/df0ee55721790ff5289d0bb0f4d584aac2f5fe13" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:11.716ex; height:2.509ex;" alt="{\displaystyle P_{0}=1~\mathrm {pW} .}"></span></dd></dl> <p>The proper notations for sound power level using this reference are <span class="nowrap"><i>L</i><sub><i>W</i>/(1 pW)</sub></span> or <span class="nowrap"><i>L</i><sub><i>W</i></sub> (re 1 pW)</span>, but the suffix notations <span class="nowrap">dB SWL</span>, <span class="nowrap">dB(SWL)</span>, dBSWL, or dB<sub>SWL</sub> are very common, even if they are not accepted by the SI.<sup id="cite_ref-NIST2008_12-0" class="reference"><a href="#cite_note-NIST2008-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup> </p><p>The reference sound power <i>P</i><sub>0</sub> is defined as the sound power with the reference sound intensity <span class="nowrap"><i>I</i><sub>0</sub> = 1 pW/m<sup>2</sup></span> passing through a surface of area <span class="nowrap"><i>A</i><sub>0</sub> = 1 m<sup>2</sup></span>: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P_{0}=A_{0}I_{0},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P_{0}=A_{0}I_{0},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0ffef4dfad7e38774df9a208fc86068c7134d775" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:11.166ex; height:2.509ex;" alt="{\displaystyle P_{0}=A_{0}I_{0},}"></span></dd></dl> <p>hence the reference value <span class="nowrap"><i>P</i><sub>0</sub> = 1 pW</span>. </p> <div class="mw-heading mw-heading3"><h3 id="Relationship_with_sound_pressure_level">Relationship with sound pressure level</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Sound_power&action=edit&section=6" title="Edit section: Relationship with sound pressure level"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The generic calculation of sound power from sound pressure is as follows: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle L_{W}=L_{p}+10\log _{10}\!\left({\frac {A_{S}}{A_{0}}}\right)\!~\mathrm {dB} ,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>W</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> <mo>+</mo> <mn>10</mn> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>10</mn> </mrow> </msub> <mspace width="negativethinmathspace" /> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>S</mi> </mrow> </msub> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mfrac> </mrow> <mo>)</mo> </mrow> <mspace width="negativethinmathspace" /> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> <mi mathvariant="normal">B</mi> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L_{W}=L_{p}+10\log _{10}\!\left({\frac {A_{S}}{A_{0}}}\right)\!~\mathrm {dB} ,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c30d56d250087daf18cc8bc9b135969f443985b3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:31.136ex; height:6.176ex;" alt="{\displaystyle L_{W}=L_{p}+10\log _{10}\!\left({\frac {A_{S}}{A_{0}}}\right)\!~\mathrm {dB} ,}"></span></dd></dl> <p>where: <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 {A_{S}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>S</mi> </mrow> </msub> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {A_{S}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/40e32c5069282f9c48d0693a15fde198b5bb6ca8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.035ex; height:2.509ex;" alt="{\displaystyle {A_{S}}}"></span> defines the area of a surface that wholly encompasses the source. This surface may be any shape, but it must fully enclose the source. </p><p>In the case of a sound source located in free field positioned over a reflecting plane (i.e. the ground), in air at ambient temperature, the sound power level at distance <i>r</i> from the sound source is approximately related to <a href="/wiki/Sound_pressure_level" class="mw-redirect" title="Sound pressure level">sound pressure level</a> (SPL) by<sup id="cite_ref-Chadderton_13-0" class="reference"><a href="#cite_note-Chadderton-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle L_{W}=L_{p}+10\log _{10}\!\left({\frac {2\pi r^{2}}{A_{0}}}\right)\!~\mathrm {dB} ,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>W</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> <mo>+</mo> <mn>10</mn> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>10</mn> </mrow> </msub> <mspace width="negativethinmathspace" /> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>2</mn> <mi>π</mi> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mfrac> </mrow> <mo>)</mo> </mrow> <mspace width="negativethinmathspace" /> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> <mi mathvariant="normal">B</mi> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L_{W}=L_{p}+10\log _{10}\!\left({\frac {2\pi r^{2}}{A_{0}}}\right)\!~\mathrm {dB} ,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/65465fb32fdd8c1c5f032bfdb07db47c75a25c3a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:32.698ex; height:6.343ex;" alt="{\displaystyle L_{W}=L_{p}+10\log _{10}\!\left({\frac {2\pi r^{2}}{A_{0}}}\right)\!~\mathrm {dB} ,}"></span></dd></dl> <p>where </p> <ul><li><i>L</i><sub><i>p</i></sub> is the sound pressure level;</li> <li><i>A</i><sub>0</sub> = 1 m<sup>2</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 {2\pi r^{2}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> <mi>π</mi> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {2\pi r^{2}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d35ad5613deaea2d77d99ef20f2a562233e689c7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:5.244ex; height:3.009ex;" alt="{\displaystyle {2\pi r^{2}},}"></span> defines the surface area of a hemisphere; and</li> <li><i>r</i> must be sufficient that the hemisphere fully encloses the source.</li></ul> <p>Derivation of this equation: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{aligned}L_{W}&={\frac {1}{2}}\ln \!\left({\frac {P}{P_{0}}}\right)\\&={\frac {1}{2}}\ln \!\left({\frac {AI}{A_{0}I_{0}}}\right)\\&={\frac {1}{2}}\ln \!\left({\frac {I}{I_{0}}}\right)+{\frac {1}{2}}\ln \!\left({\frac {A}{A_{0}}}\right)\!.\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>W</mi> </mrow> </msub> </mtd> <mtd> <mi></mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mi>ln</mi> <mspace width="negativethinmathspace" /> <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> </mtd> </mtr> <mtr> <mtd /> <mtd> <mi></mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mi>ln</mi> <mspace width="negativethinmathspace" /> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>A</mi> <mi>I</mi> </mrow> <mrow> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd /> <mtd> <mi></mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mi>ln</mi> <mspace width="negativethinmathspace" /> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>I</mi> <msub> <mi>I</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mfrac> </mrow> <mo>)</mo> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mi>ln</mi> <mspace width="negativethinmathspace" /> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>A</mi> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mfrac> </mrow> <mo>)</mo> </mrow> <mspace width="negativethinmathspace" /> <mo>.</mo> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}L_{W}&={\frac {1}{2}}\ln \!\left({\frac {P}{P_{0}}}\right)\\&={\frac {1}{2}}\ln \!\left({\frac {AI}{A_{0}I_{0}}}\right)\\&={\frac {1}{2}}\ln \!\left({\frac {I}{I_{0}}}\right)+{\frac {1}{2}}\ln \!\left({\frac {A}{A_{0}}}\right)\!.\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fb1d4f54cc007477855b683a11b699f1159800ca" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -8.671ex; width:32.914ex; height:18.509ex;" alt="{\displaystyle {\begin{aligned}L_{W}&={\frac {1}{2}}\ln \!\left({\frac {P}{P_{0}}}\right)\\&={\frac {1}{2}}\ln \!\left({\frac {AI}{A_{0}I_{0}}}\right)\\&={\frac {1}{2}}\ln \!\left({\frac {I}{I_{0}}}\right)+{\frac {1}{2}}\ln \!\left({\frac {A}{A_{0}}}\right)\!.\end{aligned}}}"></span></dd></dl> <p>For a <i>progressive</i> spherical wave, </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle z_{0}={\frac {p}{v}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>p</mi> <mi>v</mi> </mfrac> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle z_{0}={\frac {p}{v}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e9a1f2eec51561bf33d37bf38e16525088f486c6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:7.886ex; height:4.843ex;" alt="{\displaystyle z_{0}={\frac {p}{v}},}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A=4\pi r^{2},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> <mo>=</mo> <mn>4</mn> <mi>π</mi> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A=4\pi r^{2},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ba1cbdbb8a22c7db3b3f01dad4ea19f8dfcd502b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:10.086ex; height:3.009ex;" alt="{\displaystyle A=4\pi r^{2},}"></span> (the surface area of sphere)</dd></dl> <p>where <i>z</i><sub>0</sub> is the <a href="/wiki/Acoustic_impedance#Characteristic_specific_acoustic_impedance" title="Acoustic impedance">characteristic specific acoustic impedance</a>. </p><p>Consequently, </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle I=pv={\frac {p^{2}}{z_{0}}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>I</mi> <mo>=</mo> <mi>p</mi> <mi>v</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <msub> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mfrac> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I=pv={\frac {p^{2}}{z_{0}}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8d17adaba066c397d68644a98a31c9fd5ce0cc93" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:13.372ex; height:6.009ex;" alt="{\displaystyle I=pv={\frac {p^{2}}{z_{0}}},}"></span></dd></dl> <p>and since by definition <span class="nowrap"><i>I</i><sub>0</sub> = <i>p</i><sub>0</sub><sup>2</sup>/<i>z</i><sub>0</sub></span>, where <span class="nowrap"><i>p</i><sub>0</sub> = 20 μPa</span> is the reference sound pressure, </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{aligned}L_{W}&={\frac {1}{2}}\ln \!\left({\frac {p^{2}}{p_{0}^{2}}}\right)+{\frac {1}{2}}\ln \!\left({\frac {4\pi r^{2}}{A_{0}}}\right)\\&=\ln \!\left({\frac {p}{p_{0}}}\right)+{\frac {1}{2}}\ln \!\left({\frac {4\pi r^{2}}{A_{0}}}\right)\\&=L_{p}+10\log _{10}\!\left({\frac {4\pi r^{2}}{A_{0}}}\right)\!~\mathrm {dB} .\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>W</mi> </mrow> </msub> </mtd> <mtd> <mi></mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mi>ln</mi> <mspace width="negativethinmathspace" /> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <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> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mi>ln</mi> <mspace width="negativethinmathspace" /> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>4</mn> <mi>π</mi> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mfrac> </mrow> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd /> <mtd> <mi></mi> <mo>=</mo> <mi>ln</mi> <mspace width="negativethinmathspace" /> <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> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mi>ln</mi> <mspace width="negativethinmathspace" /> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>4</mn> <mi>π</mi> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mfrac> </mrow> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd /> <mtd> <mi></mi> <mo>=</mo> <msub> <mi>L</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> </mrow> </msub> <mo>+</mo> <mn>10</mn> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>10</mn> </mrow> </msub> <mspace width="negativethinmathspace" /> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>4</mn> <mi>π</mi> <msup> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <msub> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mfrac> </mrow> <mo>)</mo> </mrow> <mspace width="negativethinmathspace" /> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> <mi mathvariant="normal">B</mi> </mrow> <mo>.</mo> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}L_{W}&={\frac {1}{2}}\ln \!\left({\frac {p^{2}}{p_{0}^{2}}}\right)+{\frac {1}{2}}\ln \!\left({\frac {4\pi r^{2}}{A_{0}}}\right)\\&=\ln \!\left({\frac {p}{p_{0}}}\right)+{\frac {1}{2}}\ln \!\left({\frac {4\pi r^{2}}{A_{0}}}\right)\\&=L_{p}+10\log _{10}\!\left({\frac {4\pi r^{2}}{A_{0}}}\right)\!~\mathrm {dB} .\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/30a3f56d65bdaeeceb90893e044bc936a6562bf5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -9.505ex; width:34.473ex; height:20.176ex;" alt="{\displaystyle {\begin{aligned}L_{W}&={\frac {1}{2}}\ln \!\left({\frac {p^{2}}{p_{0}^{2}}}\right)+{\frac {1}{2}}\ln \!\left({\frac {4\pi r^{2}}{A_{0}}}\right)\\&=\ln \!\left({\frac {p}{p_{0}}}\right)+{\frac {1}{2}}\ln \!\left({\frac {4\pi r^{2}}{A_{0}}}\right)\\&=L_{p}+10\log _{10}\!\left({\frac {4\pi r^{2}}{A_{0}}}\right)\!~\mathrm {dB} .\end{aligned}}}"></span></dd></dl> <p>The sound power estimated practically does not depend on distance. The sound pressure used in the calculation may be affected by distance due to viscous effects in the propagation of sound unless this is accounted for. </p> <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_power&action=edit&section=7" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-clinical-1"><span class="mw-cite-backlink">^ <a href="#cite_ref-clinical_1-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-clinical_1-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFRonald_J._Baken,_Robert_F._Orlikoff2000" class="citation book cs1">Ronald J. Baken, Robert F. Orlikoff (2000). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=ElPyvaJbDiwC&q=sound+power+loudness&pg=PA94"><i>Clinical Measurement of Speech and Voice</i></a>. Cengage Learning. p. 94. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9781565938694" title="Special:BookSources/9781565938694"><bdi>9781565938694</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Clinical+Measurement+of+Speech+and+Voice&rft.pages=94&rft.pub=Cengage+Learning&rft.date=2000&rft.isbn=9781565938694&rft.au=Ronald+J.+Baken%2C+Robert+F.+Orlikoff&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DElPyvaJbDiwC%26q%3Dsound%2Bpower%2Bloudness%26pg%3DPA94&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASound+power" class="Z3988"></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</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.iso.org/obp/ui/#iso:std:iso:80000-8:ed-3:v1:en">"ISO 80000-8(en) Quantities and Units - Acoustics"</a>. [ISO].</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=ISO+80000-8%28en%29+Quantities+and+Units+-+Acoustics&rft.pub=%5BISO%5D&rft_id=https%3A%2F%2Fwww.iso.org%2Fobp%2Fui%2F%23iso%3Astd%3Aiso%3A80000-8%3Aed-3%3Av1%3Aen&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASound+power" 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 class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.iso.org/obp/ui/#iso:std:iso:3744:ed-3:v1:en">"ISO 3744:2010(en) Acoustics — Determination of sound power levels and sound energy levels of noise sources using sound pressure — Engineering methods for an essentially free field over a reflecting plane"</a>. [ISO]<span class="reference-accessdate">. Retrieved <span class="nowrap">22 December</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=ISO+3744%3A2010%28en%29+Acoustics+%E2%80%94+Determination+of+sound+power+levels+and+sound+energy+levels+of+noise+sources+using+sound+pressure+%E2%80%94+Engineering+methods+for+an+essentially+free+field+over+a+reflecting+plane&rft.pub=%5BISO%5D&rft_id=https%3A%2F%2Fwww.iso.org%2Fobp%2Fui%2F%23iso%3Astd%3Aiso%3A3744%3Aed-3%3Av1%3Aen&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASound+power" class="Z3988"></span></span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</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://blog.nti-audio.com/measurement/eu-sound-power-regulation-vacuum-cleaners">"EU Sound Power Regulation for Vacuum Cleaners"</a>. [NTi Audio]. 19 December 2017<span class="reference-accessdate">. Retrieved <span class="nowrap">22 December</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=EU+Sound+Power+Regulation+for+Vacuum+Cleaners&rft.pub=%5BNTi+Audio%5D&rft.date=2017-12-19&rft_id=http%3A%2F%2Fblog.nti-audio.com%2Fmeasurement%2Feu-sound-power-regulation-vacuum-cleaners&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASound+power" class="Z3988"></span></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 class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.engineeringtoolbox.com/sound-power-level-d_58.html">"Sound Power"</a>. The Engineering Toolbox<span class="reference-accessdate">. Retrieved <span class="nowrap">28 November</span> 2013</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Sound+Power&rft.pub=The+Engineering+Toolbox&rft_id=http%3A%2F%2Fwww.engineeringtoolbox.com%2Fsound-power-level-d_58.html&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASound+power" 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 class="citation web cs1"><a rel="nofollow" class="external text" href="http://www.sengpielaudio.com/calculator-soundpower.htm">"Sound Power Level"</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Sound+Power+Level&rft_id=http%3A%2F%2Fwww.sengpielaudio.com%2Fcalculator-soundpower.htm&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASound+power" 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"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAllgood2012" class="citation journal cs1">Allgood, Daniel C. (15 February 2012). <a rel="nofollow" class="external text" href="https://ntrs.nasa.gov/citations/20120003777">"NASA Technical Reports Server (NTRS)"</a>. <i>NASA</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2021-03-24</span></span>. <q>the largest sound power levels ever experienced at NASA Stennis was approximately 204dB, which corresponded to the Saturn S‐IC stage on the B‐2 test stand.</q></cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=NASA&rft.atitle=NASA+Technical+Reports+Server+%28NTRS%29&rft.date=2012-02-15&rft.aulast=Allgood&rft.aufirst=Daniel+C.&rft_id=https%3A%2F%2Fntrs.nasa.gov%2Fcitations%2F20120003777&rfr_id=info%3Asid%2Fen.wikipedia.org%3ASound+power" class="Z3988"></span></span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text">Landau & Lifshitz, "Fluid Mechanics", Course of Theoretical Physics, Vol. 6</span> </li> <li id="cite_note-IEC60027-3-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-IEC60027-3_9-0">^</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-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 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: 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=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+power" class="Z3988"></span></span> </li> <li id="cite_note-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-11">^</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-NIST2008-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-NIST2008_12-0">^</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-Chadderton-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-Chadderton_13-0">^</a></b></span> <span class="reference-text">Chadderton, David V. <i>Building services engineering</i>, pp. 301, 306, 309, 322. Taylor & Francis, 2004. <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/0-415-31535-2" title="Special:BookSources/0-415-31535-2">0-415-31535-2</a></span> </li> </ol></div></div> <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_power&action=edit&section=8" title="Edit section: External links"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="https://www.bksv.com/en/knowledge/blog/sound/sound-power-sound-pressure">Sound power and Sound pressure. Cause and Effect</a></li> <li><a rel="nofollow" class="external text" href="http://www.sengpielaudio.com/calculator-ak-ohm.htm">Ohm's Law as Acoustic Equivalent. Calculations</a></li> <li><a rel="nofollow" class="external text" href="http://www.sengpielaudio.com/RelationshipsOfAcousticQuantities.pdf">Relationships of Acoustic Quantities Associated with a Plane Progressive Acoustic Sound Wave</a></li> <li><a rel="nofollow" class="external text" href="https://wwwn.cdc.gov/niosh-sound-vibration/default.aspx">NIOSH Powertools Database</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20091112010908/http://wwwn.cdc.gov/niosh-sound-vibration/default.aspx">Archived</a> 2009-11-12 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a></li> <li><a rel="nofollow" class="external text" href="https://archive.today/20130208115754/http://www.lmsintl.com/testing/testlab/acoustics/sound-power-testing">Sound Power Testing</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 .navbox{box-sizing:border-box;border:1px solid #a2a9b1;width:100%;clear:both;font-size:88%;text-align:center;padding:1px;margin:1em auto 0}.mw-parser-output .navbox .navbox{margin-top:0}.mw-parser-output .navbox+.navbox,.mw-parser-output .navbox+.navbox-styles+.navbox{margin-top:-1px}.mw-parser-output .navbox-inner,.mw-parser-output .navbox-subgroup{width:100%}.mw-parser-output .navbox-group,.mw-parser-output .navbox-title,.mw-parser-output .navbox-abovebelow{padding:0.25em 1em;line-height:1.5em;text-align:center}.mw-parser-output .navbox-group{white-space:nowrap;text-align:right}.mw-parser-output .navbox,.mw-parser-output .navbox-subgroup{background-color:#fdfdfd}.mw-parser-output .navbox-list{line-height:1.5em;border-color:#fdfdfd}.mw-parser-output .navbox-list-with-group{text-align:left;border-left-width:2px;border-left-style:solid}.mw-parser-output tr+tr>.navbox-abovebelow,.mw-parser-output tr+tr>.navbox-group,.mw-parser-output tr+tr>.navbox-image,.mw-parser-output tr+tr>.navbox-list{border-top:2px solid #fdfdfd}.mw-parser-output .navbox-title{background-color:#ccf}.mw-parser-output .navbox-abovebelow,.mw-parser-output .navbox-group,.mw-parser-output .navbox-subgroup .navbox-title{background-color:#ddf}.mw-parser-output .navbox-subgroup .navbox-group,.mw-parser-output .navbox-subgroup .navbox-abovebelow{background-color:#e6e6ff}.mw-parser-output .navbox-even{background-color:#f7f7f7}.mw-parser-output .navbox-odd{background-color:transparent}.mw-parser-output .navbox .hlist td dl,.mw-parser-output .navbox .hlist td ol,.mw-parser-output .navbox .hlist td ul,.mw-parser-output .navbox td.hlist dl,.mw-parser-output .navbox td.hlist ol,.mw-parser-output .navbox td.hlist ul{padding:0.125em 0}.mw-parser-output .navbox .navbar{display:block;font-size:100%}.mw-parser-output .navbox-title .navbar{float:left;text-align:left;margin-right:0.5em}body.skin--responsive .mw-parser-output .navbox-image img{max-width:none!important}@media print{body.ns-0 .mw-parser-output .navbox{display:none!important}}</style></div><div role="navigation" class="navbox authority-control" aria-label="Navbox391" style="padding:3px"><table class="nowraplinks hlist navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Help:Authority_control" title="Help:Authority control">Authority control databases</a>: National <span class="mw-valign-text-top noprint" typeof="mw:File/Frameless"><a href="https://www.wikidata.org/wiki/Q1588477#identifiers" title="Edit this at Wikidata"><img alt="Edit this at Wikidata" src="//upload.wikimedia.org/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/10px-OOjs_UI_icon_edit-ltr-progressive.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/15px-OOjs_UI_icon_edit-ltr-progressive.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/20px-OOjs_UI_icon_edit-ltr-progressive.svg.png 2x" data-file-width="20" data-file-height="20" /></a></span></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="https://d-nb.info/gnd/4179361-4">Germany</a></span></li></ul></div></td></tr></tbody></table></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?useformat=desktop&type=1x1&usesul3=0" alt="" width="1" height="1" style="border: none; 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