||It has been suggested that Sound energy flux be merged into this article. (Discuss) Proposed since November 2011.|
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|Sound pressure p, SPL|
|Particle velocity v, SVL|
|Particle displacement ξ|
|Sound intensity I, SIL|
|Sound power Pac|
|Sound power level SWL|
|Sound exposure E|
|Sound exposure level SEL|
|Sound energy density E|
|Sound energy flux q|
|Acoustic impedance Z|
|Speed of sound|
|Audio frequency AF
When the acoustic wave approaches the measurement surface at an angle, the area is taken as the area times the projection of the wave direction upon the normal of the surface.
where , are the sound powers. The sound power level SWL, LW, or LPac of a source is expressed in decibels (dB) relative to a reference sound power. In air this is normally taken to be = 10−12 watt, that is 0 dB SWL.
Unlike sound pressure, sound power is neither room dependent nor distance dependent. Sound power belongs strictly to the sound source. Sound pressure is a measurement at a point in space near the source, while sound power is the total power produced by the source in all directions.
Table of selected sound sources
dB re 10−12 W
Saturn V rocket 100,000,000 200 Turbojet engine 100,000 170 Turbofan aircraft at take-off 1,000 150 Turboprop aircraft at take-off 100 140 Machine gun
Large pipe organ
10 130 Symphony orchestra
1 120 Rock concert
0.1 110 Lawn mower
Car at highway speed
.01 100 Large diesel vehicle
Heavy city traffic
0.001 90 Alarm clock 0.0001 80 Noisy office
10−5 70 Busy restaurant
10-6 60 Quiet office
10−7 50 Refrigerator
10−8 40 Quiet conversation
10−9 30 Whisper
10−10 20 Human breath 10−11 10 Threshold of hearing
Reference Power Level
Usable music sound (trumpet) and noise sound (excavator) both have the same sound power of 0.3 watts, but will be judged psychoacoustically to be different levels.
Sound power measurement
- if the source radiates sound equally in all directions into free space
- if the source is on the floor or on a wall, such that it radiates into a half sphere.
Using these equation though requires the sound pressure level to use a corresponding reference level. From the fact that the mean square sound pressure equals characteristic acoustic impedance Z0 times power per unit area, we see that if the power is measured in watts, the distance in metres, and the pressure in pascals, then we need a correction of log10Z0 with Z0 in N∙s/m3:
For air at 25°C, the impedance is 409 N∙s/m3, so this correction is −26. However, sound pressure level is usually measured against a reference of 20 μPa (introducing a correction of −94 dB), and sound power level is (as mentioned above) usually measured against a reference of 10−12 watts (introducing a correction of 120 dB). These corrections cancel, so we may use (for the case of radiation into free space):
The sound power estimated practically does not depend on distance, though theoretically it may diminish with distance due to viscous effects in the propagation of sound.
Sound power with plane sound waves
Between sound power and other important acoustic values there is the following relationship:
|c||m/s||speed of sound|
|ω = 2πf||rad/s||angular frequency|
|ρ||kg/m3||density of air|
|Z = c · ρ||N·s/m3||acoustic impedance|
|E||W·s/m3||sound energy density|
|Pac||W||sound power or acoustic 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.
where W0 is the 0 dB reference level:
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
- "Sound Power". The Engineering Toolbox. Retrieved 28 November 2013.
- Chadderton, David V. Building services engineering, pp. 301, 306, 309, 322. Taylor & Francis, 2004. ISBN 0-415-31535-2
- 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