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 measure of a ratio of two sound powers is

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

 * {| 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
 * 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
 * }
 * Excavator, trumpet || align="right" | 0.3 W || align="right" | 115 dB
 * Chain saw || align="right" | 0.1 W || align="right" | 110 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
 * }
 * 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
 * }

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
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.