Equation (9.38) can be solved for to obtain
We interpret as a signal-dependent reflection coefficient.
Since the mouthpiece of a clarinet is nearly closed, which implies and . In the limit as goes to infinity relative to , (9.42) reduces to the simple form of a rigidly capped acoustic tube, i.e., . If it were possible to open the reed wide enough to achieve matched impedance, , then we would have and , in which case , with no reflection of , as expected. If the mouthpiece is removed altogether to give (regarding it now as a tube section of infinite radius), then , , and .
Digital Waveguide Single-Reed Implementation