| Abstrakt: |
The impedance spectra of woodwind instruments with arbitrary axisymmetric geometry are studied. Piecewise interpolations of the instruments’ profile are performed, using interpolating functions amenable to analytic solutions of the Webster equation. Our algorithm optimizes on the choice of such functions, while ensuring compatibility of wave-fronts at the joining points. Employing a standard mathematical model of a single-reed mouthpiece, as well as the time-domain reflection function which is derived from our impedance results, the Schumacher equation is solved for the pressure evolution in time. Analytic checks are made to verify that, despite the nonlinearity in the reed model and in the evolution equation, solutions are unique and singularity-free. [ABSTRACT FROM AUTHOR] |
