Sound power or acoustic power is the rate at which sound energy is emitted, reflected, transmitted or received, per unit time.^[1] It is defined^[2] as "through a surface, the product of the sound pressure, and the component of the particle velocity, at a point on the surface in the direction normal to the surface, integrated over that surface." The SI unit of sound power is the watt (W).^[1] It relates to the power of the sound force on a surface enclosing a sound source, in air.

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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 sound flux or acoustic 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. The A-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.)

Sound power, denoted P, 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 vector u;
• v is the particle velocity of projection v along u;
• A is the area;
• p is the sound pressure.

In a medium, the sound power is given by

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

where

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

For example, a sound at SPL = 85 dB or p = 0.356 Pa in air (ρ = 1.2 kg⋅m⁻³ and c = 343 m⋅s⁻¹) through a surface of area A = 1 m² normal to the direction of propagation (θ = 0°) has a sound energy flux P = 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 to sound intensity:

${\displaystyle P=AI,}$

where

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

Sound power is related sound energy density:

${\displaystyle P=Acw,}$

where

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

Sound power level (SWL) or acoustic power level is a logarithmic measure of the power of a sound relative to a reference value.
Sound power level, denoted L_W and measured in dB,^[9] is defined by:^[10]

${\displaystyle L_{W}={\frac {1}{2}}\ln \!\left({\frac {P}{P_{0}}}\right)\!~\mathrm {Np} =\log _{10}\!\left({\frac {P}{P_{0}}}\right)\!~\mathrm {B} =10\log _{10}\!\left({\frac {P}{P_{0}}}\right)\!~\mathrm {dB} ,}$

where

• P is the sound power;
• P₀ is the reference sound power;
• 1 Np = 1 is the neper;
• 1 B = 1/2 ln 10 is the bel;
• 1 dB = 1/20 ln 10 is the decibel.

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

${\displaystyle P_{0}=1~\mathrm {pW} .}$

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

The reference sound power P₀ is defined as the sound power with the reference sound intensity I₀ = 1 pW/m² passing through a surface of area A₀ = 1 m²:

${\displaystyle P_{0}=A_{0}I_{0},}$

hence the reference value P₀ = 1 pW.