Sound Wave of “Stable” Form

Sound waves of finite amplitude are subject to progressive distortion or change in form during propagation. Theoretical analysis of this phenomenon for a plane wave neglecting dissipative forces leads ultimately to a multiple valued solution for acoustic pressure, displacement, etc. This is inconsistent with fact. R. D. Fay, introducing viscosity into the analysis, arrived at a solution in which the progressive distortion is balanced by the dissipative effects of viscosity. This wave, called the “stable” form, is essentially sawtoothed, varying in sharpness depending upon its intensity. Experimental measurements in a free spherically-diverging sound field verify the existence of the stable wave by showing the progressive distortion of an initially sinusoidal wave to a sawtoothed stable form. Comparison of the experimental results (for the diverging field) with the theoretical results (for a plane wave field) reveals good agreement as to the harmonic content of the stable form, except that a higher sound intensity is required in the diverging field. Both experimentally and theoretically, for sufficiently high intensities, the pressure amplitude of the nth harmonic relative to that of the fundamental approaches 1/n.