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Sound power level

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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 level or acoustic power level is a logarithmic measure of the sound power in comparison to a specified reference level.

The measure of a ratio of two sound powers is [Sound Power, Sound Intensity, and the difference between the two - Indiana University's High Energy Physics Department] [Georgia State University Physics Department - Tutorial on Sound Intensity]

[L_\mathrm=10\, \log_\left(\frac\right)\ \mathrm]
where W1 and W0 are the powers.

The sound power level is given the symbol Lw or SWL and is measured in "dBW", which stands for decibel with the suffix for watts. Decibels are dimensionless. SPL stands for sound pressure level, and is not the same thing.

If W0 is the standard reference sound power, where

[W_0=10^\ \mathrm]
(W = watt), then instead of "dB", dB SWL is used. (SWL = sound power level).

Table: Sound power level and sound power 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

The Trumpet and excavator both have the same sound power of 0.3 watts, but may be judged psychoacoustically to be different levels. As noise is unwanted sound the trumpet can be percieved to be acceptable when listened to as music but at the same sound power level may be percieved to be noisy if one is trying to sleep.

References

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