Approximate formulas are given for the natural wavelengths associated with the free radial vibration of a thick-walled, infinitely long, hollow cylinder. For the radial extensional mode, the wavelength is nearly proportional to the nth-order mean radius, where n depends on Poisson's ratio. For the thickness modes, a correction factor is derived which may be applied to the plane-wave solution. The extensional solution is also applied to the case of a thin, flat washer.
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J. A. McFadden (1954) studied this question.