A simplified diagram of the clarinet mouthpiece is shown in Fig. 9.40. The pressure in the mouth is assumed to be a constant value , and the bore pressure is defined located at the mouthpiece. Any pressure drop across the mouthpiece causes a flow into the mouthpiece through the reed-aperture impedance which changes as a function of since the reed position is affected by . To a first approximation, the clarinet reed can be regarded as a spring flap regulated Bernoulli flow (§B.7.5), ). This model has been verified well experimentally until the reed is about to close, at which point viscosity effects begin to appear . It has also been verified that the mass of the reed can be neglected to first order,10.18 so that is a positive real number for all values of . Possibly the most important neglected phenomenon in this model is sound generation due to turbulence of the flow, especially near reed closure. Practical synthesis models have always included a noise component of some sort which is modulated by the reed , despite a lack of firm basis in acoustic measurements to date.
The fundamental equation governing the action of the reed is continuity of volume velocity, i.e.,
In operation, the mouth pressure
and incoming traveling bore pressure
are given, and the reed computation must produce an outgoing bore
which satisfies (9.35), i.e., such that
It is helpful to normalize (9.38) as follows: Define , and note that , where . Then (9.38) can be multiplied through by and written as , or
An example of the qualitative appearance of overlaying is shown in Fig. 9.41.