# 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.

The sound power level of a signal with sound power "W" is [ [http://hep.physics.indiana.edu/~rickv/Sound_intensity.html Sound Power, Sound Intensity, and the difference between the two - Indiana University's High Energy Physics Department] ] [ [http://hyperphysics.phy-astr.gsu.edu/Hbase/sound/db.html Georgia State University Physics Department - Tutorial on Sound Intensity] ] :$L_mathrm\left\{W\right\}=10, log_\left\{10\right\}left\left(frac\left\{W\right\}\left\{W_0\right\} ight\right) mathrm\left\{dB\right\}$

where "W"0 is the 0 dB SWL reference level::$W_0=10^\left\{-12\right\} mathrm\left\{W\right\}$

The sound power level is given the symbol "L"W or SWL. This is not to be confused with dBW, which 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:$mathit\left\{SWL\right\} = mathit\left\{SPL\right\}+10, log_\left\{10\right\}left\left(frac\left\{4pi r^2\right\}\left\{S_0\right\} ight\right)$where $S_0 = 1 m^2$.

This is only valid assuming the acoustic impedance of the medium equals 400 Pa*s/m.

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

:

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.

SWL in audio equipment

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.

References

* [http://www.sengpielaudio.com/calculator-ak-ohm.htm Ohm's law as acoustic equivalent - calculator]
* [http://www.sengpielaudio.com/ConnectionOfAcousticSizes.pdf Formulas - Connection of acoustic sizes for even progressive acoustic waves -pdf]
* [http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=JASMAN000094000004002194000001&idtype=cvips&gifs=yes Radiation modes and the active control of sound power - Journal Article: Acoustical Society of America]

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