#### Scattering-Theoretic Formulation

Equation (9.38) can be solved for to obtain

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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Computational Methods

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Digital Waveguide Single-Reed Implementation