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Plane-Wave Scattering

Consider a plane-wave $ p^+_1$ propagating from wave impedance $ R_1$ into a new wave impedance $ R_2$ :

\epsfig{file=eps/planewavescat.eps}

Physical constraints:

\begin{eqnarray*}
p^+_1+p^-_1 &=& p^+_2\quad\mbox{(pressure continuous across junction)}\\
v^{+}_1+v^{-}_1 &=& v^{+}_2\quad\mbox{(velocity in = velocity out)}
\end{eqnarray*}

Ohm's Law relations:

\begin{displaymath}
\begin{array}{rcrl}
p^+_i&=&&R_iv^{+}_i\\
p^-_i&=&-&R_iv^{-}_i
\end{array}\end{displaymath}



Subsections
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``Scattering at an Impedance Discontinuity'', by Julius O. Smith III, (From Lecture Overheads, Music 420).
Copyright © 2015-05-19 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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