Self-Sustained Oscillations in Clarinet-Like Systems—Quantitative Results
Walter E. Worman · The Journal of the Acoustical Society of America · 1970
Quantitative results are presented of calculations (based on the formalism discussed by the author at the 1968 Cleveland meeting) for a system composed of a clarinet reed and mouthpiece attached to a clarinet-like tube. The impedance curve of this tube has one peak (QZ0) and one dip (Z0/Q), which lie below the cutoff frequency supplied by a row of open holes. Above cutoff, the impedance Z ≅ Z0, the characteristic impedance of the tube. The Q of the tube is 13.5. Calculation deals with medium and small amplitudes of oscillation, i.e., when the reed does not beat. The frequency of steady-state oscillation and the pressure spectrum (amplitudes and phases) in the mouthpiece are found as a function of blowing pressure, starting from the measured impedance curve of the tube, and dynamical coefficients of the reed, with Backus' measurements of nonlinear flow through a clarinet mouthpiece as a function of reed opening and pressure difference across it. The threshold blowing pressure is also calculated. Numerical results are in accord with experimental observation.