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Sound intensity

sound intensity, sound intensity equation
Sound intensity also known as acoustic intensity is defined as the power carried by 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 quantity1

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


  • 1 Mathematical definition
  • 2 Inverse-square law
  • 3 Sound intensity level
  • 4 Measurement
  • 5 References
  • 6 External links

Mathematical definitionedit

Sound intensity, denoted I, is defined by

I = p v =p\mathbf


  • 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

⟨ I ⟩ = 1 T ∫ 0 T p t v t d t \rangle =\int _^pt\mathbf t\,\mathrm t Also, Intensity of Sound = 2π²n²A²ρv Where, n is frequency of sound, A is the Amplitude of sound wave, v is velocity of sound, and ρ is density of medium in which sound is traveling

Inverse-square lawedit

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

I r = P A r = P 4 π r 2 , =,


  • P is the sound power;
  • Ar is the area of a sphere of radius r

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

I r ∝ 1 r 2

This relationship is an inverse-square law

Sound intensity leveledit

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 dB, and defined by2

L I = 1 2 ln I I 0   N p = log 10 I I 0   B = 10 log 10 I I 0   d B , =\ln \!\left\right\!~\mathrm =\log _\!\left\right\!~\mathrm =10\log _\!\left\right\!~\mathrm ,


  • I is the sound intensity;
  • I0 is the reference sound intensity;
  • 1 Np = 1 is the neper;
  • 1 B = 1/2 ln10 is the bel;
  • 1 dB = 1/20 ln10 is the decibel

The commonly used reference sound intensity in air is3

I 0 = 1   p W / m 2 =1~\mathrm

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, dBSIL, dBSIL, or dBSIL are very common, even if they are not accepted by the SI4

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

I ∝ p 2

The equality of SIL and SPL requires that

I I 0 = p 2 p 0 2 , =^,

where p0 = 20 μPa is the reference sound pressure

For a progressive spherical wave,

p v = z 0 , =z_,

where z0 is the characteristic specific acoustic impedance Thus,

I 0 = p 0 2 I p 2 = p 0 2 p v p 2 = p 0 2 z 0 =^I=^pv=^

In air at ambient temperature, z0 = 410 Pa·s/m, hence the reference value I0 = 1 pW/m25

In an anechoic chamber, which approximates a free field no reflection, the SIL can be taken as being equal to the SPL 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 crosspower6


  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 30, 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 87, "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
  6. ^ Sound Intensity Theory

External linksedit

  • How Many Decibels Is Twice as Loud Sound Level Change and the Respective Factor of Sound Pressure or Sound Intensity
  • Acoustic Intensity
  • Conversion: Sound Intensity Level to Sound Intensity and Vice Versa
  • Ohm's Law as Acoustic Equivalent Calculations
  • Relationships of Acoustic Quantities Associated with a Plane Progressive Acoustic Sound Wave
  • Table of Sound Levels Corresponding Sound Intensity and Sound Pressure
  • What Is Sound Intensity Measurement and Analysis

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