|Sound pressure||p, SPL,LPA|
|Particle velocity||v, SVL|
|Sound intensity||I, SIL|
|Sound power||P, SWL, LWA|
|Sound energy density||w|
|Sound exposure||E, SEL|
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.
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
- p is the sound pressure;
- v is the particle velocity.
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
- is frequency of sound,
- is the amplitude of the sound wave particle displacement,
- is density of medium in which sound is traveling, and
- is speed of sound.
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
- P is the sound power;
- A(r) is the surface area of a sphere of radius r.
Thus sound intensity decreases as 1/r2 from the centre of the sphere:
This relationship is an inverse-square law.
Sound intensity 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
- I is the sound intensity;
- I0 is the reference sound intensity;
The commonly used reference sound intensity in air is
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.
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.
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. 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.
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
On the other hand, the bias error introduced by a p-u probe can be approximated by
- ^ "Sound Intensity". Retrieved 22 April 2015.
- ^ "Letter symbols to be used in electrical technology – Part 3: Logarithmic and related quantities, and their units", IEC 60027-3 Ed. 3.0, International Electrotechnical Commission, 19 July 2002.
- ^ Ross Roeser, Michael Valente, Audiology: Diagnosis (Thieme 2007), p. 240.
- ^ Thompson, A. and Taylor, B. N. sec 8.7, "Logarithmic quantities and units: level, neper, bel", Guide for the Use of the International System of Units (SI) 2008 Edition, NIST Special Publication 811, 2nd printing (November 2008), SP811 PDF
- ^ Sound Power Measurements, Hewlett Packard Application Note 1230, 1992.
- ^ Fahy, Frank (2017). Sound Intensity. CRC Press. ISBN 978-1138474192. OCLC 1008875245.
- ^ Jacobsen, Finn (2013-07-29). Fundamentals of general linear acoustics. ISBN 9781118346419. OCLC 857650768.
- ^ a b c Jacobsen, Finn; de Bree, Hans-Elias (2005-09-01). "A comparison of two different sound intensity measurement principles" (PDF). The Journal of the Acoustical Society of America. 118 (3): 1510–1517. Bibcode:2005ASAJ..118.1510J. doi:10.1121/1.1984860. ISSN 0001-4966. S2CID 56449985.