Sound power oracoustic power is the rate at whichsound energy is emitted,reflected,transmitted or received, per unit time.^[1] It is defined^[2] as "through a surface, the product of thesound pressure, and the component of theparticle velocity, at a point on the surface in the directionnormal to the surface,integrated over that surface." TheSI unit of sound power is thewatt (W).^[1] It relates to the power of the sound force on a surface enclosing a sound source, in air.

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 calledsoundflux oracoustic flux through that area.

Regulations often specify a method for measurement^[3] that integrates sound pressure over a surface enclosing the source.L_WA 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. TheA-weighting scale is used in the calculation as the metric is concerned with the loudness as perceived by the human ear. Measurements^[4] 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.)

Here is a table of some examples, from an on-line source.^[5] For omnidirectional point sources in free space, sound power inL_WA is equal tosound pressure level in dB above 20 micropascals at a distance of 0.2821 m^[6]

Sound power, denotedP, is defined by^[8]

${\displaystyle P=\mathbf{f}\cdot \mathbf{v}=Ap\mathbf{u}\cdot \mathbf{v}=Apv}$

where

• f is the sound force of unit vectoru;
• v is theparticle velocity of projectionv alongu;
• A is the area;
• p is thesound pressure.

In amedium, the sound power is given by

${\displaystyle P=\frac{A{p}^2}{\rho c}\cos \theta ,}$

where

• A is the area of the surface;
• ρ is themass density;
• c is thesound velocity;
• θ is the angle between the direction of propagation of the sound and the normal to the surface.
• p is thesound pressure.

For example, a sound at SPL = 85 dB orp = 0.356 Pa in air (ρ =1.2 kg⋅m⁻³ andc =343 m⋅s⁻¹) through a surface of areaA =1 m² normal to the direction of propagation (θ = 0°) has a sound energy fluxP =0.3 mW.

This is the parameter one would be interested in when converting noise back into usable energy, along with any losses in the capturing device.

Sound power is related tosound intensity:

${\displaystyle P=AI,}$

where

• A stands for the area;
• I stands for the sound intensity.

Sound power is relatedsound energy density:

${\displaystyle P=Acw,}$

where

• c stands for thespeed of sound;
• w stands for the sound energy density.

Sound power level (SWL) oracoustic power level is alogarithmic measure of the power of a sound relative to a reference value.
Sound power level, denotedL_W and measured indB,^[9] is defined by:^[10]

${\displaystyle L_W=\frac{1}{2}\ln \left(\frac{P}{P_0}\right)\mathrm{N}\mathrm{p}={\log }_{10}\left(\frac{P}{P_0}\right)\mathrm{B}=10{\log }_{10}\left(\frac{P}{P_0}\right)\mathrm{d}\mathrm{B},}$

where

• P is the sound power;
• P₀ is thereference sound power;
• 1 Np = 1 is theneper;
• 1 B =⁠1/2⁠ ln 10 is thebel;
• 1 dB =⁠1/20⁠ ln 10 is thedecibel.

The commonly used reference sound power in air is^[11]

${\displaystyle P_0=1\mathrm{p}\mathrm{W}.}$

The proper notations for sound power level using this reference areL_{W/(1 pW)} orL_W (re 1 pW), but the suffix notationsdB SWL,dB(SWL), dBSWL, or dB_SWL are very common, even if they are not accepted by the SI.^[12]

The reference sound powerP₀ is defined as the sound power with the reference sound intensityI₀ = 1 pW/m² passing through a surface of areaA₀ = 1 m²:

${\displaystyle P_0=A_0{I}_0,}$

hence the reference valueP₀ = 1 pW.

The generic calculation of sound power from sound pressure is as follows:

${\displaystyle L_W=L_p+10{\log }_{10}\left(\frac{A_S}{A_0}\right)\mathrm{d}\mathrm{B},}$

where:${\displaystyle A_S}$ defines the area of a surface that wholly encompasses the source. This surface may be any shape, but it must fully enclose the source.

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 distancer from the sound source is approximately related tosound pressure level (SPL) by^[13]

${\displaystyle L_W=L_p+10{\log }_{10}\left(\frac{2\pi r^2}{A_0}\right)\mathrm{d}\mathrm{B},}$

where

• L_p is the sound pressure level;
• A₀ = 1 m²;
• ${\displaystyle 2\pi r^2,}$ defines the surface area of a hemisphere; and
• r must be sufficient that the hemisphere fully encloses the source.

Derivation of this equation:

For aprogressive spherical wave,

${\displaystyle z_0=\frac{p}{v},}$

${\displaystyle A=4\pi r^2,}$ (the surface area of sphere)

wherez₀ is thecharacteristic specific acoustic impedance.

Consequently,

${\displaystyle I=pv=\frac{p^2}{z_0},}$

and since by definitionI₀ =p₀²/z₀, wherep₀ = 20 μPa is the reference sound pressure,

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.

• Sound power and Sound pressure. Cause and Effect
• Ohm's Law as Acoustic Equivalent. Calculations
• Relationships of Acoustic Quantities Associated with a Plane Progressive Acoustic Sound Wave
• NIOSH Powertools DatabaseArchived 2009-11-12 at theWayback Machine
• Sound Power Testing

• Acoustics
• Sound
• Sound measurements
• Physical quantities
• Power (physics)

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