Functional model of a simplified clarinet

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.