Sound Power - Sound Power Level

Sound power level or acoustic power level is a logarithmic measure of the sound power in comparison to a specified reference level. While sound pressure level is given in decibels SPL, or dB SPL, sound power is given in dB SWL. The dimensionless term "SWL" can be thought of as "sound watts level," the acoustic output power measured relative to 10−12 or 0.000000000001 watt (1 pW). As used by architectural acousticians to describe noise inside a building, typical noise measurements in SWL are very small, less than 1 watt of acoustic power.

The sound power level of a signal with sound power W is:

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

where W0 is the 0 dB reference level:

W_0=10^{-12}\ \mathrm{W}=1\ \mathrm{pW}\,

The sound power level is given the symbol LW. This is not to be confused with dBW, which is a measure of electrical power, and uses 1 W as a reference level.

In the case of a free field sound source in air at ambient temperature, the sound power level is approximately related to sound pressure level (SPL) at distance r of the source by the equation

L_\mathrm{p} = L_\mathrm{W}+10\, \log_{10}\left(\frac{S_0}{4\pi r^2}\right)\,

where . This assumes that the acoustic impedance of the medium equals 400 Pa·s/m.

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