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Moving Termination: Ideal String


\begin{center}
\epsfig{file=eps/fMovingTermPhysical.eps,width=6.5in} \\
Uniformly moving rigid termination for an ideal string\\
(tension $K$, mass density $\epsilon $) at time $0<t_0<L/c$.
\end{center}
Driving-Point Impedance $ F_0/V_0$ :

\begin{eqnarray*}
y'(t_0,0) &=&
-\frac{v_0 t_0}{c t_0} =
-\frac{v_0}{c} =
-\frac{v_0}{\sqrt{K/\epsilon }} \\ [10pt]
\Rightarrow\quad
f_0 &=& -K\sin(\theta)\approx -Ky'(t,0) = \sqrt{K\epsilon }\,v_0 \mathrel{\stackrel{\mathrm{\Delta}}{=}}R\, v_0
\end{eqnarray*}

\begin{center}
\epsfig{file=eps/moveterm.eps,width=6.5in} \\
\end{center}



Subsections
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``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
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