The single-reed woodwind excitation mechanism can be reasonably well modeled as a nonlinear spring because it is normally driven well below its resonance frequency.
Using DW techniques, this characteristic is transformed into a nonlinear reflection function and implemented via a scattering junction as shown in Fig. 22. The pressure entering the downstream instrument air column is determined as:
is the nonlinear reed reflection coefficient.
Details regarding the derivation of
in the context of a traveling-wave, scattering theory approach are available elsewhere Smith (1986); Scavone (1997).
Pressure scattering on the upstream side of the reed junction is given by