Sound power

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Sound measurements
Sound pressure p
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
Surface S
Acoustic impedance Z
Speed of sound c
v • d • e

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}

where

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.

[edit] Table: Sound power and sound power level of some sound sources

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

[edit] Sound power with plain sound waves

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

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

[edit] External links