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 P_ac
Sound power level (SWL)
Sound energy density E
Sound energy flux q
Acoustic impedance Z
Speed of sound c

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.

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

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.

[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
P_ac	W	sound power or acoustic power
A	m²	area