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Other Wave Variables
(Wave-Impedance Preview)

Transverse Velocity Waves:

\begin{eqnarray*}
v^{+}(n) &\mathrel{\stackrel{\mathrm{\Delta}}{=}}& \dot y^{+}(n)\\
v^{-}(n) &\mathrel{\stackrel{\mathrm{\Delta}}{=}}& \dot y^{-}(n)
\end{eqnarray*}

Wave Impedance (we'll derive later):

$\displaystyle \zbox{R = \sqrt{K\epsilon } = \frac{K}{c} = \epsilon c}
$

Force Waves:

\begin{eqnarray*}
f^{{+}}(n) &\mathrel{\stackrel{\mathrm{\Delta}}{=}}& R\,v^{+}(n)\\
f^{{-}}(n) &\mathrel{\stackrel{\mathrm{\Delta}}{=}}& -R\,v^{-}(n)
\end{eqnarray*}

Ohm's Law for Traveling Waves:

\fbox{%
\begin{minipage}[c]{3in}%
\begin{displaymath}\begin{array}{rcrl}%
f^{{+}}(n)&=&&R\,v^{+}(n) \\
f^{{-}}(n)&=&-&R\,v^{-}(n)
\end{array}\end{displaymath}\end{minipage}}


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Download StringWaves.pdf
Download StringWaves_2up.pdf
Download StringWaves_4up.pdf

``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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