THEORY OF THE ATTENUATION OF VERY HIGH AMPLITUDE SOUND WAVES
Abstract:
A discussion is given of the propagation of continuous plane progressive sound waves with pressure variations of the order of one-tenth the average pressure. Shocks are shown to develop at the leading front of each wave after several wave lengths of propagation regardless of the initial wave form. The attenuation of the repeated shocks was derived from shock wave theory with the assumption that the resulting stable wave form is saw-tooth in character. Writing P2P1 1 delta, where P1 - P2 is the pressure discontinuity at the shock, it is shown that 1delta - 1delta omicro gamma 12 gamma . X - Xo, lambda where sigma o is the value of sigma at the distance Xo, gamma is the ratio of specific heats, and lambda is the wave length of the sound. The result was compatible with previously published studies of the attenuation of single N- shaped waves. Fays solution J. Acoust. Soc. America 2222, 1931 of the hydrodynamic equations including the effects of viscosity, which shows the stable wave form to be a saw tooth, may be extended to yield the derived attenuation rate.