Sound measurements | |
---|---|
Characteristic | Symbols |
Sound pressure | p, SPL, LPA |
Particle velocity | v, SVL |
Particle displacement | δ |
Sound intensity | I, SIL |
Sound power | P, SWL, LWA |
Sound energy | W |
Sound energy density | w |
Sound exposure | E, SEL |
Acoustic impedance | Z |
Audio frequency | AF |
Transmission loss | TL |
Sound intensity, also known as acoustic intensity, is defined as the power carried by sound waves per unit area in a direction perpendicular to that 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.[1]
Sound intensity is not the same physical quantity as sound pressure. Human hearing is 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.
Sound intensity level is a logarithmic expression of sound intensity relative to a reference intensity.
Sound intensity, denoted I, is defined by
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
Further information: Inverse-square law |
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
Thus sound intensity decreases as 1/r2 from the centre of the sphere:
This relationship is an inverse-square law.
For other uses, see Sound level. |
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 nepers, bels, or decibels, and defined by[2]
The commonly used reference sound intensity in air is[3]
being approximately the lowest sound intensity hearable by an undamaged human ear under room conditions. 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.[4]
The reference sound intensity I0 is defined such that a progressive plane wave has the same value of sound intensity level (SIL) and sound pressure level (SPL), since
The equality of SIL and SPL requires that
For a progressive spherical wave,
In air at ambient temperature, z0 = 410 Pa·s/m, hence the reference value I0 = 1 pW/m2.[5]
In an anechoic chamber which approximates a free field (no reflection) with a single source, measurements in the far field in SPL can be considered to be equal to measurements in SIL. This fact is exploited to measure sound power in anechoic conditions.
Sound intensity is defined as the time averaged product of sound pressure and acoustic particle velocity.[6] Both quantities can be directly measured by using a sound intensity p-u probe comprising a microphone and a particle velocity sensor, or estimated indirectly by using a p-p probe that approximates the particle velocity by integrating the pressure gradient between two closely spaced microphones.[7]
Pressure-based measurement methods are widely used in anechoic conditions for noise quantification purposes. The bias error introduced by a p-p probe can be approximated by[8]
On the other hand, the bias error introduced by a p-u probe can be approximated by[8]