Scattering Formulation

Solve for $p_b^{-}$ to obtain

$$\begin{eqnarray*} p_b^{-}&=& \frac{1-r}{1+r}p_b^{+}+ \frac{r}{1+r}p_m\\ [10pt] ... ...p_m\\ [10pt] &=& \frac{p_m}{2} - \rho \frac{p_{\Delta}^{+}}{2} \end{eqnarray*}$$

where

$$\begin{eqnarray*} \rho(p_{\Delta}) &\mathrel{\stackrel{\mathrm{\Delta}}{=}}& \fr... ...) &=& \hbox{\emph{signal-dependent reflection coef\-fi\-cient.}} \end{eqnarray*}$$

In practice, $R_m\gg R_b\;\Rightarrow\; r\approx 0, \rho\approx 1$
(mouthpiece looks largely like a closed end)