Next  |  Prev  |  Top  |  JOS Index  |  JOS Pubs  |  JOS Home  |  Search

Force Waves

\epsfbox{eps/fStringForce.eps}

To unify vibrating strings with acoustic tubes, we choose the force which acts to the right as our force wave variable:

$\displaystyle f(t,x) \mathrel{\stackrel{\mathrm{\Delta}}{=}}f_r(t,x) = \zbox{-Ky'(t,x)}
$

For acoustic tubes, we have

\begin{displaymath}
\begin{array}{rcrl}
p^+(n) &=& &R_{\hbox{\tiny T}}\, u^{+}(n) \\
p^-(n) &=& -&R_{\hbox{\tiny T}}\, u^{-}(n)
\end{array}\end{displaymath}

where


Next  |  Prev  |  Top  |  JOS Index  |  JOS Pubs  |  JOS Home  |  Search

Download VariableChoice.pdf
Download VariableChoice_2up.pdf
Download VariableChoice_4up.pdf

``Choice of Wave Variables in Digital Waveguide Models'', by Julius O. Smith III, (From Lecture Overheads, Music 420).
Copyright © 2019-02-05 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
CCRMA  [Automatic-links disclaimer]