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Traveling-Wave Solution

One-dimensional lossless wave equation:

$\displaystyle \zbox{ Ky''= \epsilon {\ddot y}}
$

Plug in traveling wave to the right:

\begin{eqnarray*}
y(t,x) &=& y_r(t-x/c) \\
& & \\
\Rightarrow \quad
y'(t,x) &=& -\frac{1}{c}{\dot y}(t,x) \\
y''(t,x) &=& \;\;\;\frac{1}{c^2}{\ddot y}(t,x)
\end{eqnarray*}



Subsections
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Download StringWaves.pdf
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Download StringWaves_4up.pdf

``Digitizing Strings Waves in Vibrating Strings'', by Julius O. Smith III, (From Lecture Overheads, Music 420).
Copyright © 2015-05-02 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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