Finite‐Amplitude Acoustic Waves in Nonlinear Relaxing Media

The problem of propagation of finite‐amplitude acoustic waves in nonlinear media is studied by the method of small perturbations in acoustic Mach number M. Depending upon the dispersion parameter σ = (C∞2 − C02)/C∞2, which measures the coupling between acoustic and relaxation processes, the system of pertubation equations takes two distinct forms. This distinction is analogous to that which occurs in viscous fluids, where the critical parameter is the Reynolds number [Z. A. Goldberg, Sov. Phys. Acoust. 2, (1956)]. For σ≪M, the perturbation equations are typical of those for non‐dissipative media whose solutions are characterized by continued harmonic amplitude growth with propagation distance, indicative of shock formation. For the case where σ≫M, solutions are obtained correct to second order, taking account of the second‐order boundary conditions. The second harmonic and phase‐shifted wavenumbers agree with those obtained by Polyakova [Sov. Phys. Acoust. 6, (1960)]. The amplitude of the second harmonic ...