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Sampled Traveling Waves in a String

For discrete-time simulation, we must sample the traveling waves

For a vibrating string with length $ L$ and fundamental frequency $ f_0$,

$\displaystyle c = f_0 \cdot 2L
\quad\quad \left(\frac{\hbox{periods}}{\hbox{se...
...\frac{\hbox{meters}}{\hbox{period}}
= \frac{\hbox{meters}}{\hbox{sec}}\right)
$

so that

$\displaystyle X= cT = (f_0 2L)/f_s= L [ f_0 / (f_s/2) ]
$

Thus, the number of spatial samples along the string is

$\displaystyle L/X= (f_s/2) / f_0
$

or

$\displaystyle \hbox{Number of spatial samples} = \hbox{Number of string harmonics}
$

Examples:


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Download WaveEquations.pdf
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Download WaveEquations_4up.pdf

``Distributed Modeling in Discrete Time'', by Julius O. Smith III and Nelson Lee,
REALSIMPLE Project — work supported by the Wallenberg Global Learning Network .
Released 2008-06-05 under the Creative Commons License (Attribution 2.5), by Julius O. Smith III and Nelson Lee
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
CCRMA