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Ideal Vibrating String


Wave Equation

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

K& \mathrel{\stackrel{\Delta}{=}}& \hb...
...a}{=}}& \frac{\partial}{\partial x}y(t,x) \nonumber

Newton's second law

$\displaystyle \zbox{\hbox{Force} = \hbox{Mass} \times \hbox{Acceleration}}


Example One-Dimensional Waveguides

Let's first review the finite difference approximation applied to the ideal string (for comparison purposes):

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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