Sound power or acoustic power P_ac is a measure of sonic energy E per time t unit.
It is measured in watts, or sound intensity I times area A:

$$

P_{\mathrm{acoustic}} = I \cdot A

The measure of a ratio of two sound powers is

$$

L_\mathrm{w}=10\, \log_{10}\left(\frac{P_1}{P_0}\right)\ \mathrm{dB}

where

P₁, P₀ are the sound powers.

The sound power level PWL, L_W, or L_Pac of a source is expressed in decibels (dB) and is equal to 10 times the logarithm to the base 10 of the ratio of the sound power of the source to a reference sound power. It is thus a logarithmic measure.

The reference sound power in air is normally taken to be 10⁻¹² watt = 0 dB SWL.

Sound power is neither room dependent nor distance dependent, like it is with sound pressure or sound intensity. Sound power belongs strictly to the sound source. There is no decrease of power with distance.

Table: Sound power and sound power level of some sound sources

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{| class="wikitable"

! Situation
and
sound source !! sound power
P_ac
watts !! sound power
level L_w
dB re 10^-12 W Rocket engine 1,000,000 W 180 dB Turbojet engine 10,000 W 160 dB Siren 1,000 W 150 dB Heavy truck engine or
loudspeaker rock concert 100 W 140 dB Machine gun 10 W 130 dB Jackhammer 1 W 120 dB Excavator, trumpet 0.3 W 115 dB Chain saw 0.1 W 110 dB Helicopter 0.01 W 100 dB Loud speech,
vivid children 0.001 W 90 dB Usual talking,
Typewriter 10⁻⁵ W 70 dB Refrigerator 10⁻⁷ W 50 dB (Auditory threshold) 10^-12 W 0 dB

Usable music sound (trumpet) and noise sound (excavator) have both the same sound power of 0.3 watts, but will be judged psychoacoustically to be different levels.

Sound power with plain sound waves

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Between sound power and other important acoustic values there is the following relationship:

$P\_\{ak\}\; =\; \backslash xi^2\; \backslash cdot\; \backslash omega^2\; \backslash cdot\; Z\; \backslash cdot\; A\; =\; v^2\; \backslash cdot\; Z\; \backslash cdot\; A\; =\; \backslash frac\{a^2\; \backslash cdot\; Z\; \backslash cdot\; A\}\{\backslash omega^2\}\; =\; \backslash frac\{p^2\; \backslash cdot\; A\}\{Z\}\; =\; E\; \backslash cdot\; c\; \backslash cdot\; A\; =\; I\; \backslash cdot\; A$

where:

Symbol	Units	Meaning
p	Pa	sound pressure
f	Hz	frequency
ξ	m	particle displacement
c	m/s	speed of sound
v	m/s	particle velocity
ω = 2πf	rad/s	angular frequency
ρ	kg/m3	density of air
Z = c · ρ	N·s/m³	acoustic impedance
a	m/s²	particle acceleration
I	W/m²	sound intensity
E	W·s/m³	sound energy density
Pac	W	sound power or acoustic power
A	m²	area

External links

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• Ohm's law of the acoustics - calculations
• Connection of acoustic sizes for even progressive acoustic waves

Measurement | Power | Sound

Schallleistung | Potencia acústica