ACOUSTIC RESONATORS WITH VARIABLE NONUNIFORMITY

In a novel set of acoustic resonators, alterations of the nonuniformit y in cross-sectional area are utilized to change the resonance frequen cy. Each resonator is designed to yield two, three, or four frequencie s whose differences correspond to musical intervals. The apparatus hav e a simple piecewise-uniform geometry that can easily be changed, and are useful as educational demonstrations of an effect of nonuniformity on waves. The shifts in frequency can be accurately calculated by imp osing boundary conditions on solutions of the wave equation in the uni form regions. The phenomenon can be physically understood with the ene rgy method of Rayleigh, or more generally with the method of adiabatic invariance. The latter methods yield the shift in resonance frequency for arbitrary but small nonuniformity.