On the instability of one-dimensional acoustic standing waves

Abstract

The paper theoretically considers the instability of acoustical standing waves in a nondispersive medium in a plane-parallel layer excited at the border of the layer or by a distributed force. The instability is caused by the nonlinear resonance interaction that sets in motion the parametric temporal amplification of the spontaneously formed standing waves. Discussion will focus on the results of the deviation of the frequencies of the parametrically excited subharmonic waves from the natural frequencies of the layer. This phenomenon was noted by a number of investigators [L. Adler and M. A. Breazeale, J. Acoust. Soc. Am. 48, 1077–1083 (1970); N.-C. Yen, J. Acoust. Soc. Am. 57, 1357–1362 (1975); Z. A. Goldberg, in ProblemsofNonlinearAcoustics, XIth Int. Symp. on Nonlinear Acoustics (in Russian), Part I (SO AN USSR, Novosibirsk, 1987), pp. 154–158]. It is shown that this phenomenon is not connected with the borders of the layer but it is peculiar to waves running in opposite directions that replaced the standing wave. The cause of these results is the instability of the standing waves to waves with deviated frequencies.