Scattering-Theoretic Formulation
Equation (9.38) can be solved for to obtain
where
![]() |
(10.44) |
We interpret
![$ \rho(p_{\Delta})$](http://www.dsprelated.com/josimages_new/pasp/img2352.png)
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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Digital Waveguide Single-Reed Implementation