#### Scattering-Theoretic Formulation

Equation (9.38) can be solved for to obtain

 (10.41) (10.42) (10.43)

where
 (10.44)

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 .

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