Abstract
Nonlinear acoustic theory is used to show that the cutoff frequencies and the resonant frequencies of modes in acoustic waveguides of finite length depend upon the mode amplitude. The amplitude εn, of mode n > 0, produced by a periodic piston motion of amplitude δn, is also determined. It is found that at and near a resonant frequency, εn≏δn1/3 while at and near the cutoff frequency εn≏δn1/2. Away from these frequencies εn≏δn, as linear theory predicts. Thus the infinite amplitude, which linear theory yields at cutoff and resonance, is avoided. The results are obtained simply by using the result for the propagation constant as a function of mode amplitude given by J. B. Keller and M. H. Millman [J. Acoust. Soc. Am. 49, 329–333(1971)].
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