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Expanded Wave Digital Mass-Spring Oscillator

\begin{figure}\centering \input fig/tankwdf.pstex_t \\ \end{figure}

Wave variables to Physical Variables:

\begin{eqnarray*} f_k(n) &=& f^{{+}}_k(n) + f^{{-}}_k(n) \qquad\hbox{(Spring For... ...f_m(n) &=& f^{{+}}_m(n) + f^{{-}}_m(n) \qquad\hbox{(Mass Force)} \end{eqnarray*}

Reflection coefficient:

$\displaystyle \rho = \frac{m-k}{m+k} $

(Impedance step over impedance sum from one infinitesimal waveguide to the next.)

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Download SMAC03S.pdf
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``Recent Developments in Musical Sound Synthesis Based on a Physical Model'', by Julius O. Smith III, (Stockholm Musical Acoustics Conference (SMAC-03), August 6--9, 2003).
Copyright © 2006-02-19 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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