Dept. of Eng. Sci., Hokkaido Univ., Sapporo 060, Japan
The propagation of weakly nonlinear plane waves emitted from a harmonically oscillating plate into an ideal gas of semi-infinite extent is considered under the condition that the energy dissipation is negligibly small everywhere except for discontinuous shock fronts. Recently, the authors have numerically shown that, in the case of strongly nonlinear waves, contrary to the result of the conventional weakly nonlinear theory, streaming due to shocks occurs in the direction of wave propagation and thereby the gas near the source is rarefied as time proceeds [Y. Inoue and T. Yano, J. Acoust. Soc. Am. 94, 1632--1642 (1993)]. In the present paper, the evolution of the weakly nonlinear waves including shocks is determined up to O(M[sup 2]), where M is the acoustic Mach number (M<<1). In this order, the wave profile develops to an asymmetrical sawtoothlike one in the far field and weak streaming is excited in the region beyond the shock formation distance. For M(less than or approximately equal to)0.2, the results quantitatively agree with those in the previous work. Furthermore, by taking into account both the production of entropy and the generation of reflected wave at each shock front, the physical mechanism is clarified for the rarefaction of the gas in O(M[sup 3]).