# Sound power level

34,200pages on
this wiki

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 [1] [2]

$L_\mathrm{W}=10\, \log_{10}\left(\frac{W_1}{W_0}\right)\ \mathrm{dB}$

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 an amount of sound power at a particular frequency produces a particular sound pressure level x, the same amount of power at half the frequency will produce twice the pressure level.

If W0 is the standard reference sound power, where

$W_0=10^{-12}\ \mathrm{W}$

(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 Edit

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
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 perceived to be acceptable when listened to as music but at the same sound power level may be perceived to be noisy if one is trying to sleep.

One of the advantages of expressing the noise level of a source in terms of its power level is that one does not have to note any distance from the source. A noise sound pressure level, say, 85 dB-A is meaningless unless one also notes the distance from the source where the measurement was made.

### SWL in audio equipment Edit

Most audio manufacturers use SWL to describe the efficiency of their speakers. The most common means is measuring the sound power level from the speaker with the measuring device placed directly in front of and one meter away from the source. Then a particular sound (usually white noise or pink noise) is played through the source at a particular intensity so that the source is consuming one watt of power. The SWL is then measured and the product labeled, something like "SWL: 93 dB 1 W/1 m". This measurement can also be represented as a strict efficiency ratio of audio output (sound power) to electrical input (electrical power), but this is far less common. This method of rating speakers using SWL is often deceiving because most speakers produce very different SWLs at different frequencies of sound, often varying as much as ±10 dB throughout the speaker's usable frequency range (it generally varies less in higher quality speakers). The SWL quoted by the manufacturer is often an average over a particular range.