Sound power

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.

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

 * {| class="wikitable"

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