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Acoustic Intensity

Acoustic Intensity (a real vector) may be defined by

$\displaystyle \zbox{\underline{I} \mathrel{\stackrel{\mathrm{\Delta}}{=}}p \underline{v}}
\quad \left(\frac{\mbox{\large Energy Flux}}{\mbox{\large Area}\cdot\mbox{\large Time}} =
\frac{\mbox{\large Power Flux}}{\mbox{\large Area}}\right)
$

where

\begin{eqnarray*}
p &=& \mbox{acoustic pressure} \quad \left(\frac{\mbox{\large Force}}{\mbox{\large Area}}\right)\\
\underline{v}&=& \mbox{acoustic particle velocity} \quad \left(\frac{\mbox{\large Length}}{\mbox{\large Time}}\right)
\end{eqnarray*}

For a traveling plane wave, we have

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

where

$\displaystyle R \mathrel{\stackrel{\mathrm{\Delta}}{=}}\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{\large Mass}}{\mbox{\large Volume}}\right)\\
v &\mathrel{\stackrel{\mathrm{\Delta}}{=}}& \left\vert\underline{v}\right\vert
\end{eqnarray*}

Therefore, in a plane wave,

$\displaystyle \zbox{I \;\mathrel{\stackrel{\mathrm{\Delta}}{=}}\;p v \;=\;Rv^2 \;=\;\frac{p^2}{R}}
$


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Download Delay.pdf
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``Computational Acoustic Modeling with Digital Delay'', by Julius O. Smith III, (From Lecture Overheads, Music 420).
Copyright © 2014-03-24 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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