Acoustic Intensity

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Acoustic Intensity

Acoustic intensity may be defined by

$\displaystyle \zbox {\underline{I} \;\isdef \; p \underline{v}} \quad \left(\fr... ...ox{\small Time}} = \frac{\mbox{\small Power Flux}}{\mbox{\small Area}}\right)$

where

$\begin{eqnarray*} p &=& \mbox{acoustic pressure} \quad \left(\frac{\mbox{\small ... ...ad \left(\frac{\mbox{\small Length}}{\mbox{\small Time}}\right). \end{eqnarray*}$

For a plane traveling wave, we have

$\displaystyle \zbox {p = R v}$

where

$\displaystyle \zbox {R \;\isdef \; \rho c}$

is called the wave impedance of air, and

$\begin{eqnarray*} c &=& \mbox{sound speed},\\ \rho &=& \mbox{mass density of ai... ...ume}}\right),\\ v &\isdef & \left\vert\underline{v}\right\vert. \end{eqnarray*}$

Therefore, in a plane wave,

$\displaystyle \zbox {I = p v = Rv^2 = \frac{p^2}{R}.}$

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written by Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.

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Physical Audio Signal Processing
    Elementary Physics, Mechanics, and Acoustics
       Properties of Gases
          Acoustic Intensity