- Alternately, the reed mechanism can be viewed as having a ``lumped,'' pressure dependent impedance given by:

(26) - Under the assumption that the reed motion is adequately described as ``stiffness dominated'' and in-phase with the driving pressure and that the resulting volume flow through the reed slit is also frequency-independent (ignoring the inertance of the air in the reed channel), this characterization can be evaluated in the time domain as a memory-less non-linearity.
- Viewing the reed/air column junction using scattering theory as seen from the air column side, pressure-wave reflection from an impedance of
*Z*_{R}is given by:

- The reed interface is then modeled with a nonlinear pressure-dependent reflection coefficient (
) given by Eq. (28) and implemented via a scattering junction as shown in Fig. 13. The pressure entering the downstream instrument air column is determined as (Smith, 1986):

*p*_{d}^{+}= = (29)

- The reflection coefficient defined by the Bernoulli flow expression of Eq. (22) is shown in Fig. 14.
**Figure 14:**Reed/air column reflection coefficient values for different values of equilibrium tip opening (*H*). - For values of
, the pressure reflection coefficient has unity gain. This corresponds to reflection from a rigidly stopped end, as mentioned previously.
- A coefficient value of zero corresponds to a junction without discontinuity.
- A coefficient of -1.0 corresponds to an ideally open-pipe end (a reed mechanism of zero impedance).
- For normal reed mechanisms with a narrow-slit geometry, it seems impossible that the reed/bore junction could ever be characterized by a reflection coefficient of zero or lower. It is expected that the impedance of the reed slit, even when unblown, has some minimum value (probably frequency-dependent, but we'll ignore that for now) greater than
*Z*_{c}.

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