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Sound power

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Sound measurements
Sound pressure p
Sound pressure level (SPL)
Particle velocity v
Particle velocity level (SVL)
   (Sound velocity level)
Particle displacement ξ
Sound intensity I
Sound intensity level (SIL)
Sound power Pac
Sound power level (SWL)
Sound energy density E
Sound energy flux q
Acoustic impedance Z
Speed of sound c

Sound power or acoustic power Pac 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}


P1, P0 are the sound powers.

The sound power level PWL, LW, or LPac 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.

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

sound source
sound power
sound power
level Lw
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,
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) both have the same sound power of 0.3 watts, but will be judged psychoacoustically to be different levels.

Sound power with plain sound wavesEdit

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

P_{ak} = \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


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 Edit


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