Propagating and Standing Sawtooth Waves

Abstract

The well-known theory for energy dissipation in weak shock waves is applied to the case of propagating and standing acoustic waves of finite amplitude. The known results for the decay of plane, cylindrical, and spherical waves propagating in a fluid are obtained by means of a simple technique previously used by Rudnick [J. Acoust. Soc. Amer. 25, 1012 (L) (1953)] and based on the assumption that the waves are of the sawtooth type with a weak discontinuity each wavelength. The same technique is then applied to large-amplitude resonant oscillations in tubes, assuming that the acoustic field can be represented by two sawtooths traveling in opposite directions inside the tube. These calculations are of a very simple nature and yield solutions that compare favorably with results obtained by more rigorous techniques.