Multifrequency acoustic resonators with variable nonuniformity
Alkov, Steven L.
Denardo, Bruce C.
Atchley, Anthony A.
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A new type of acoustic resonator utilizes alterations of the nonuniformity to achieve different resonance frequencies. Each resonator is designed to yield frequencies that correspond to musical notes. The apparatus are remarkably simple, employing piecewise uniform cross sectional areas that can easily and quickly be changed. The resonators are thus useful as educational demonstrations. The phenomenon can be understood physically and quantified perturbatively by the energy method or Rayleigh, or equivalently by the method of adiabative invariance. Improved accuracy is obtained by matching one-dimensional solutions of the wave equation in the uniform regions. The agreement between this theory and the experimental data is less than one percent.
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