Abstract
In a novel set of acoustic resonators, alterations of the nonuniformity in cross-sectional area are utilized to change the resonance frequency. Each resonator is designed to yield two, three, or four frequencies whose differences correspond to musical intervals. The apparatus have 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 imposing boundary conditions on solutions of the wave equation in the uniform regions. The phenomenon can be physically understood with the energy 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.
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