Ab initio calculations of the oscillations of a clarinet
Robert T. Schumacher · The Journal of the Acoustical Society of America · 1979
The internal oscillating functions volume velocity, pressure, and reed displacement have been calculated for a clarinet. The data used, all in the literature, are the mechanical properties of the reed, the geometrical measurements of the instrument, the properties of air, properties of tone holes [A. H. Benade, J. Acoust. Soc. Am. 41, 1609 (1967)], and data and calculations on the flow of air through a slit. From these, the input impedance Z(ω) is calculated, and is used to find an effective reflection function r(t). The latter is used in an algorithm [first used in calculating bowed string oscillations: M. E. McIntyre and J. Woodhouse, Acoustica 41 (in press)] that permits rapid numerical integration of the integral equations of motion of the system. The normal behavior of clarinets is observed in both chalumeau and clarion registers. Multiphonics are also calculated. Steady state behavior agrees qualitatively with the previous calculations [R. T. Schumacher, Acustica 40, 298 (1978)] to the extent that the latter are comparable with the present more elaborate model.