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| {{merge from|Sound energy flux|discuss=Talk:Sound_power#Another_merge_proposal|date=November 2011}}
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| {{Refimprove|date=October 2008}}
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| {{Sound measurements}}
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| '''Sound power''' or '''acoustic power''' ''P''<sub>ac</sub> is a measure of [[sound energy]] ''E'' per [[time]] ''t'' unit. It is measured in [[watt]]s and can be computed as [[sound intensity]] (''I'') times area (''A''):
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| :<math>
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| P_{\mathrm{acoustic}} = I \cdot A
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| </math>
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| When the acoustic wave approaches the measurement surface at an angle, the area is taken as the area times the projection of the wave direction upon the normal of the surface.
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| The difference between two sound powers can be express in [[decibel]]s ([[logarithmic scale|logarithmic measure]]) using this equation:
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| :<math>
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| L_\mathrm{w}=10\, \log_{10}\left(\frac{P_1}{P_0}\right)\ \mathrm{dB}
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| </math>
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| where <math>P_1</math>, <math>P_0</math> are the sound powers. The '''sound power level''' SWL, ''L''<sub>W</sub>, or ''L''<sub>Pac</sub> of a source is expressed in [[decibel]]s (dB) relative to a reference sound power. In air this is normally taken to be <math>{P_0}\,</math> = 10<sup>−12</sup> watt, that is 0 dB SWL.
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| Unlike sound pressure, sound power is neither room dependent nor distance dependent. Sound power belongs strictly to the sound source. Sound pressure is a measurement at a point in space near the source, while sound power is the total power produced by the source in all directions.
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| == Table of selected sound sources==
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| :{| class="wikitable"
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| ! Situation<br>and<br>sound source !! sound power<br>''P''<sub>ac</sub><br>watts !! sound power<br>level ''L''<sub>w</sub><br>dB re 10<sup>−12</sup> W
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| |-
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| | [[Saturn V]] rocket || align="right" | '''100,000,000''' || align="right" | 200
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| |-
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| | [[Turbojet]] engine || align="right" | '''100,000''' || align="right" | 170
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| |-
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| | [[Turbofan]] aircraft at take-off || align="right" | '''1,000''' || align="right" | 150
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| |-
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| | [[Turboprop]] aircraft at take-off || align="right" | '''100''' || align="right" | 140
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| |-
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| | [[Machine gun]] <br>Large [[pipe organ]]|| align="right" | '''10''' || align="right" | 130
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| |-
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| | [[Symphony orchestra]]<br>Heavy [[thunder]]<br>[[Sonic boom]] || align="right" | '''1''' || align="right" | 120
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| |-
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| | [[Rock concert]]<br>[[Chain saw]]<br>Accelerating [[motorcycle]]|| align="right" | '''0.1''' || align="right" | 110
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| |-
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| | [[Lawn mower]]<br>Car at highway speed<br>[[Subway]] || align="right" | '''.01''' || align="right" | 100
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| |-
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| | Large [[diesel vehicle]]<br>Heavy city traffic || align="right" | '''0.001''' || align="right" | 90
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| | Alarm clock || align="right" | '''0.0001''' || align="right" | 80
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| |-
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| | Noisy office<br>Vacuum cleaner || align="right" | '''10<sup>−5</sup>''' || align="right" | 70
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| |-
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| | Busy restaurant<br>Hair dryer || align="right" | '''10<sup>-6</sup>''' || align="right" | 60
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| | Quiet office<br>Average home|| align="right" | '''10<sup>−7</sup>''' || align="right" | 50
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| | [[Refrigerator]]<br>low voice<br>Quiet home || align="right" | '''10<sup>−8</sup>''' || align="right" | 40
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| |-
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| | Quiet conversation <br>Broadcast studio|| align="right" | '''10<sup>−9</sup>''' || align="right" | 30
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| | Whisper<br>Wristwatch ticking|| align="right" | '''10<sup>−10</sup>''' || align="right" | 20
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| | Human breath || align="right" | '''10<sup>−11</sup>''' || align="right" | 10
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| |-
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| | [[Threshold of hearing]]<br>Reference Power Level || align="right" | '''10<sup>−12</sup>''' || align="right" | 0
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| |}
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| <ref>{{cite web | url = http://www.engineeringtoolbox.com/sound-power-level-d_58.html | title = Sound Power | publisher = The Engineering Toolbox | accessdate = 28 November 2013 }}</ref>
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| Usable music sound (trumpet) and noise sound (excavator) both have the same sound power of 0.3 watts, but will be judged [[psychoacoustics|psychoacoustically]] to be different levels.
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| ==Sound power measurement==
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| A frequently used method of estimating the sound power level of a source <math>(L_\mathrm{W})</math> is to measure the [[sound pressure level]] <math>(L_\mathrm{p})</math> at some distance <math>r</math>, and solve for <math>L_\mathrm{W}</math>:{{Citation needed|date=November 2009}}
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| :<math>
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| L_\mathrm{W} = L_\mathrm{p}-10\, \log_{10}\left(\frac{1}{4\pi r^2}\right)\,
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| </math> if the source radiates sound equally in all directions into free space
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| or
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| :<math>
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| L_\mathrm{W} = L_\mathrm{p}-10\, \log_{10}\left(\frac{2}{4\pi r^2}\right)\,
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| </math> if the source is on the floor or on a wall, such that it radiates into a half sphere.
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| Using these equation though requires the sound pressure level to use a corresponding reference level. From the fact that the mean square sound pressure equals [[characteristic acoustic impedance]] Z<sub>0</sub> times power per unit area, we see that if the power is measured in watts, the distance in metres, and the pressure in pascals, then we need a correction of log<sub>10</sub>Z<sub>0</sub> with Z<sub>0</sub> in N∙s/m<sup>3</sup>:
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| :<math>L_\mathrm{W} = L_\mathrm{p}-10\, \log_{10}\left(\frac{1}{4\pi r^2}\right)\,-\log_{10}Z_0</math>
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| For air at 25°C, the impedance is 409 N∙s/m<sup>3</sup>, so this correction is −26. However, sound pressure level is usually measured against a reference of 20 μPa (introducing a correction of −94 dB), and sound power level is (as mentioned above) usually measured against a reference of 10<sup>−12</sup> watts (introducing a correction of 120 dB). These corrections cancel, so we may use (for the case of radiation into free space):
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| :<math>\text{dBSWL} = \text{dBSPL}+10\, \log_{10}\left(4\pi r^2\right)</math>
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| The sound power estimated practically does not depend on distance, though theoretically it may diminish with distance due to viscous effects in the propagation of sound.
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| ==Sound power with plane sound waves==
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| Between sound power and other important acoustic values there is the following relationship:
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| :<math>
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| P_\mathrm{ac} = \xi^2 \cdot \omega^2 \cdot Z \cdot A = v^2 \cdot Z \cdot A = \frac{a^2 \cdot Z \cdot A}{\omega^2} = \frac{p^2 \cdot A}{Z} = E \cdot c \cdot A = I \cdot A\,
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| </math>
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| where:
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| {| class="wikitable"
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| ! Symbol !! Units !! Meaning
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| |-
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| ! ''p''
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| | [[Pascal (unit)|Pa]] || [[sound pressure]]
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| |-
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| ! ''f''
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| | [[Hertz|Hz]] || [[frequency]]
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| |-
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| ! ''ξ''
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| | [[Metre|m]]|| [[particle displacement]]
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| |-
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| ! ''c''
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| | [[Metre|m]]/[[second|s]] || [[speed of sound]]
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| |-
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| ! ''v''
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| | [[meters per second|m/s]] || [[particle velocity]]
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| |-
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| ! ω = 2π''f''
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| | [[radian|rad]]/[[second|s]] || [[angular frequency]]
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| |-
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| ! ''ρ''
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| | [[kilogram|kg]]/[[Metre|m]]<sup>3</sup> || [[density of air]]
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| |-
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| ! ''Z = c · ρ''
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| | [[newton (unit)|N]]·[[second|s]]/[[Metre|m]]<sup>3</sup> || [[acoustic impedance]]
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| |-
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| ! ''a''
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| | [[Metre|m]]/[[second|s]]<sup>2</sup> || [[particle acceleration]]
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| |-
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| ! ''I''
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| | [[Watt|W]]/m<sup>2</sup> || [[sound intensity]]
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| |-
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| ! ''E''
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| | [[Watt|W]]·[[second|s]]/[[Metre|m]]<sup>3</sup> || [[sound energy density]]
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| |-
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| ! ''P''<sub>ac</sub>
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| | [[Watt|W]] || sound power or [[acoustic power]]
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| |-
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| ! ''A''
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| | [[Metre|m]]<sup>2</sup> || [[area]]
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| |}
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| ==Sound power level==<!--[[Sound power level]] and [[Template:Sound measurements]] redirect directly here.-->
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| '''Sound power level''' or '''acoustic power level''' is a [[logarithmic scale|logarithmic measure]] of the sound power in comparison to a specified reference level. While [[sound pressure level]] is given in decibels SPL, or dB SPL, sound power is given in dB SWL. The dimensionless term "SWL" can be thought of as "sound watts level,"<ref name=Chadderton/> the acoustic output power measured relative to 10<sup>−12</sup> or 0.000000000001 [[watt]] (1 pW). As used by [[Architectural acoustics|architectural acousticians]] to describe noise inside a building, typical noise measurements in SWL are very small, less than 1 watt of acoustic power.<ref name=Chadderton/>
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| The sound power level of a signal with sound power ''W'' is:<ref>[http://hep.physics.indiana.edu/~rickv/Sound_intensity.html Sound Power, Sound Intensity, and the difference between the two - Indiana University's High Energy Physics Department]</ref><ref>[http://hyperphysics.phy-astr.gsu.edu/Hbase/sound/db.html Georgia State University Physics Department - Tutorial on Sound Intensity]</ref>
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| :<math>
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| L_\mathrm{W}=10\, \log_{10}\left(\frac{W}{W_0}\right)\ \mathrm{dB}\,
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| </math>
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| where ''W''<sub>0</sub> is the 0 dB reference level:
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| :<math>
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| W_0=10^{-12}\ \mathrm{W}=1\ \mathrm{pW}\,
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| </math>
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| The sound power level is given the symbol ''L''<sub>W</sub>. This is not to be confused with [[decibel watt|dBW]], which is a measure of electrical power, and uses 1 W as a reference level.
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| In the case of a free field sound source in air at ambient temperature, the sound power level is approximately related to [[sound pressure level]] (SPL) at distance ''r'' of the source by the equation
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| :<math>
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| L_\mathrm{p} = L_\mathrm{W}+10\, \log_{10}\left(\frac{S_0}{4\pi r^2}\right)\,
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| </math>
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| where <math>S_0 = 1\ \mathrm{m}^2</math>.<ref name=Chadderton>Chadderton, David V. ''Building services engineering'', pp. 301, 306, 309, 322. Taylor & Francis, 2004. ISBN 0-415-31535-2</ref> This assumes that the [[acoustic impedance]] of the medium equals 400 Pa·s/m.
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| == References == | |
| <references />
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| == External links ==
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| *[http://www.sengpielaudio.com/SoundPressureAndSoundPower.pdf Sound power and Sound pressure – Cause and Effect]
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| *[http://www.sengpielaudio.com/calculator-ak-ohm.htm Ohm's law as acoustic equivalent — calculations]
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| *[http://www.sengpielaudio.com/RelationshipsOfAcousticQuantities.pdf Relationships of acoustic quantities associated with a plane progressive acoustic sound wave — pdf]
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| *[http://wwwn.cdc.gov/niosh-sound-vibration/default.aspx NIOSH Powertools Database]
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| *[http://www.lmsintl.com/testing/testlab/acoustics/sound-power-testing Sound Power Testing]
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| [[Category:Power (physics)]]
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| [[Category:Sound measurements]]
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