With a few exceptions Sommerfeldt and Strong (1988); Keefe (1990b), most wind instrument simulations have assumed a constant or slowly varying pressure in the player's mouth and otherwise ignored possible upstream influences.
Under these assumptions, the upstream system can be considered a large reservoir driven by a zero-frequency (DC) current source.
An electrical circuit analog for such a system is shown in Fig. 23. The current source Ul represents the player's lungs, while flow resistance in the lungs and trachea is characterized by Rl.
Electrical circuit analog for a traditional upstream windway system.
In general, the lung impedance varies over time based on the vocal fold configuration.
The cavity impedance is given by
, where is the mass density of air, c is the speed of sound in air, V is the volume of the cavity, and is the radian frequency.
The upstream resistance parameter Ru characterizes losses in the player's windway.
The impedance seen by the reed looking upstream is infinite for steady flow but relatively small at higher frequencies.
Under these conditions, the reed is controlled by the oscillating pressure on its downstream side and the DC upstream pressure only.