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Sound intensity

Sound measurements
Characteristic
Symbols
 Sound pressure  p, SPL
 Particle velocity  v, SVL
 Particle displacement  δ
 Sound intensity  I, SIL
 Sound power  P, SWL
 Sound energy  W
 Sound energy density  w
 Sound exposure  E, SEL
 Acoustic impedance  Z
 Speed of sound  c
 Audio frequency  AF
 Transmission loss  TL


Sound intensity also known as acoustic intensity is defined as the Energy carried by the sound waves per unit area. The SI unit of intensity, which includes sound intensity, is the watt per square meter (W/m2). One application is the noise measurement of sound intensity in the air at a listener's location as a sound energy quantity.

Sound intensity is not the same physical quantity as sound pressure. Hearing is directly sensitive to sound pressure which is related to sound intensity. In consumer audio electronics, the level differences are called "intensity" differences, but sound intensity is a specifically defined quantity and cannot be sensed by a simple microphone. The rate at which sound energy passes through a unit area held perpendicular to the direction of propagation of sound waves is called intensity of sound.

Sound intensity, denoted I, is defined by

where

Both I and v are vectors, which means that both have a direction as well as a magnitude. The direction of sound intensity is the average direction in which energy is flowing.

The average sound intensity during time T is given by

For a spherical sound wave, the intensity in the radial direction as a function of distance r from the centre of the sphere is given by

where

Thus sound intensity decreases as 1/r2 from the centre of the sphere:

This relationship is an inverse-square law.

Sound intensity level (SIL) or acoustic intensity level is the level (a logarithmic quantity) of the intensity of a sound relative to a reference value.
It is denoted LI, expressed in dB, and defined by

where

The commonly used reference sound intensity in air is

The proper notations for sound intensity level using this reference are LI /(1 pW/m2) or LI (re 1 pW/m2), but the notations dB SIL, dB(SIL), dBSIL, or dBSIL are very common, even if they are not accepted by the SI.


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