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Acoustic Intensity

Acoustic intensity may be defined by

$\displaystyle \zbox {\underline{I} \isdefs p \underline{v}}
\quad \left(\frac{\mbox{\small Energy Flux}}{\mbox{\small Area}\cdot\mbox{\small Time}}
\eqsp
\frac{\mbox{\small Power Flux}}{\mbox{\small Area}}\right)
$

where

\begin{eqnarray*}
p &=& \mbox{acoustic pressure} \quad \left(\frac{\mbox{\small Force}}{\mbox{\small Area}}\right)\\
\underline{v}&=& \mbox{acoustic particle velocity} \quad \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 \isdefs \rho c}
$

is called the wave impedance of air, and

\begin{eqnarray*}
c &=& \mbox{sound speed},\\
\rho &=& \mbox{mass density of air} \quad \left(\frac{\mbox{\small Mass}}{\mbox{\small Volume}}\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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``Physical Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2010, ISBN 978-0-9745607-2-4.
Copyright © 2014-06-11 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
CCRMA