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Acoustic Plane Waves

Pressure Plane Waves:

\begin{eqnarray*}
p^+(n) &\mathrel{\stackrel{\mathrm{\Delta}}{=}}& R_a\,u^{+}(n)\\
p^-(n) &\mathrel{\stackrel{\mathrm{\Delta}}{=}}& -R_a\,u^{-}(n)
\end{eqnarray*}

where $ u^{+},u^{-}$ are
Longitudinal Particle-Velocity Waves




Ohm's Law for Traveling Acoustic Plane Waves:

\fbox{%
\begin{minipage}[c]{3in}%
\begin{displaymath}\begin{array}{rcrl}%
p^+(n)&=&& R_au^{+}(n) \\
p^-(n)&=&-& R_au^{-}(n)
\end{array}\end{displaymath}\end{minipage}}
where

$\displaystyle \zbox{R_a = \rho c}
$

is the wave impedance of air in terms of mass density $ \rho$ ( kg$ /$m$ ^3$ ) and sound speed $ c$ .


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``Digitizing Strings Waves in Vibrating Strings'', 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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