Functional model of a simplified clarinet

Abstract

A functional model of a simplified clarinet has been developed and implemented on a digital computer. The simplified clarinet consists of a standard clarinet mouthpiece and reed attached to a straight cylindrical tube. In the model, the tube and mouthpiece are represented by a lumped element approximation to a transmission line and the reed is represented as a nonuniform bar, clamped at one end. Differential equations for the system are solved numerically on a digital computer to obtain pressures and volume velocities of the air in the tube and mouthpiece, and positions of the reed at successive time increments. The model exhibits self-sustained oscillations, threshold blowing pressures, frequency shifts, and spectra of mouthpiece and radiated pressures which are similar to those of an actual simplified clarinet. A previously unreported dependence of volume velocity in the reed aperture on the initial or rest opening of the aperture was also found.