Peter L. Hoekje
Dept. of Phys., Univ. of Northern Iowa, Cedar Falls, IA 50614-0150
A numerical model is designed in order to predict playing frequencies of air reed instruments. The air reed mechanism is modeled by dynamically solving the Navier--Stokes equation for an incompressible fluid over a two-dimensional grid in the vicinity of the jet outlet, the edge on which the jet impinges, and a short distance into the main bore. The rest of the main bore is modeled as a quasi-one-dimensional waveguide, represented by an impulse response function. At the junction between the two parts of the model, the exciting wavefront is typically bulged, so the velocity distribution must be integrated over the bore cross section in order to calculate the excitation of the main bore. The results confirm that mode locking and octave overblowing occur in an instrument whose frequency response has nearly harmonic resonances, but not in one whose second resonance is much higher than twice the first resonance frequency. Comparisons of the resulting playing frequencies with experimental playing frequencies, and with those calculated by a simple passive model, will be presented.