Plane-Wave Scattering

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

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:

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