When the amplitude of an acoustic wave at its source becomes sufficiently large, new phenomena due to nonlinearity appear. The main effect of nonliniarity is a distortion of the wave profile, so that the spectral form of the wave changes in comparison with its original form. The studies of such changes for waves of different waveforms, propagating through media of different constitution and in different geometries, is a field of research which has developed much since the second world war, partly because of the possibility to use nonlinear sound eftects tor emitting and receiving signals [l]. The present article gives an account for some recent developments of the theory of nonlinear sound propagation in simple media with simple geometries and waveforms.

The nonlinear theory of acoustic waves is founded on the fundamental hydrodynamical equations together with a constitutive equation of the medium. In this paper we start with these equations and derive a general nonlinear wave equation (Kuznetsov’s equation), by means of which equations for all types of waves later treated in this paper are derived.