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the plane wave expression for the sound Intensity was lacking a source and not precisely defined. Depending if one takes the peak value of the sound pressure or the effective sound pressure there is a factor of 2 involved (see Beranek which I added as a source)) Tag: Reverted |
m →Measurement: - Added internal link to wiki page of particle velocity probe |
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The average sound intensity during time ''T'' is given by
<math display="block">\langle \mathbf I\rangle = \frac{1}{T} \int_0^T p(t) \mathbf v(t) \,\mathrm{d}t.</math>
For a plane wave {{Citation needed|reason=This is a special case of the above expression, link to the derivation is needed|date=August 2022}},
<math display="block">\Iota = 2\pi^2\nu^2 \delta
Where,
* <math>\nu</math> is frequency of sound,
* <math>\delta</math> is the
* <math>\rho</math> is density of medium in which sound is traveling, and
* <math>c</math> is speed of sound.
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==Measurement==
Sound intensity is defined as the time averaged product of sound pressure and acoustic particle velocity.<ref>{{Cite book | title=Sound Intensity| last=Fahy | first = Frank| date=2017 | publisher=CRC Press| isbn=978-1138474192|oclc=1008875245}}</ref> Both quantities can be directly measured by using a sound intensity ''p-u'' probe comprising a microphone and a [[Particle velocity probe|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.<ref>{{Cite book | title=Fundamentals of general linear acoustics | last=Jacobsen | first = Finn | isbn=9781118346419 | oclc=857650768 | date = 2013-07-29}}</ref>
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<ref name=":0">{{Cite journal |last1=Jacobsen|first1=Finn |last2=de Bree|first2=Hans-Elias |date=2005-09-01 |title=A comparison of two different sound intensity measurement principles |journal=The Journal of the Acoustical Society of America |volume=118 |issue=3 |pages=1510–1517 |doi=10.1121/1.1984860 |bibcode=2005ASAJ..118.1510J |s2cid=56449985 |issn=0001-4966 |url=https://backend.orbit.dtu.dk/ws/files/4449916/Jacobsen.pdf}}</ref>
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