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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 measurements
 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
 Speed of sound c
 Audio frequency AF
 Transmission loss TL

Sound intensity is not the same physical quantity as sound pressure. Human 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.

Sound intensity level is a logarithmic expression of sound intensity relative to a reference intensity.


Mathematical definitionEdit

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

  is frequency of sound,
  is the amplitude of the sound wave particle displacement,
  is speed of sound, and
  is density of medium in which sound is traveling

Inverse-square lawEdit

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.

Sound intensity levelEdit

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]



  • I is the sound intensity;
  • I0 is the reference sound intensity;
  • 1 Np = 1 is the neper;
  • 1 B = (1/2) ln(10) is the bel;
  • 1 dB = (1/20) ln(10) is the decibel.

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


where p0 = 20 μPa is the reference sound pressure.

For a progressive spherical wave,


where z0 is the characteristic specific acoustic impedance. Thus,


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.


One method of sound intensity measurement involves the use of two microphones located close to each other, normal to the direction of sound energy flow. A signal analyser is used to compute the crosspower between the measured pressures and the sound intensity is derived from (proportional to) the imaginary part of the crosspower.


  1. ^ "Sound Intensity". Retrieved 22 April 2015.
  2. ^ "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.
  3. ^ Ross Roeser, Michael Valente, Audiology: Diagnosis (Thieme 2007), p. 240.
  4. ^ 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
  5. ^ Sound Power Measurements, Hewlett Packard Application Note 1230, 1992.

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