The dispersion effects appearing during the propagation of acoustic waves through the plasma of a weakly ionized gas are studied. The main theoretical results are based on the equation of propagation of sound in the medium with the so called Rayleigh energy release mechanism, which has been obtained earlier.Unlike the previous investigations, the problem of propagation of a perturbation from a source and not the problem of propagation of the initial perturbation is solved. In particular, the sources of an N shaped shock wave and a wave in the form of a symmetrical step are analyzed in detail. It is shown that depending on the direction of wave propagation (along or across the electric field in a plasma), it degenerates either into a wave packet with a wave frequency lower than a certain frequency characterizing heating, or into a wave packet with a frequency higher than this value. In addition, a quantitative criterion is obtained, which makes it pos sible to estimate the plasma parameters for which it will be possible to observe the dispersion of acoustic waves in the plasma.

This research continues theoretical studies of propagation of acoustic waves in a plasma consider ing it in the context of a Rayleigh medium. For the first time, the solution to the problem with the boundary and not the initial conditions is examined. It is shown that for small values of the parameter characterizing the energy input in the plasma, the amplification coefficients of a harmonic acoustic wave in the problem of propagation of the initial perturbation and in the problem with the boundary conditions are close. However, if the energy input increases, the amplification of the wave propagating from the source is larger than in the problem of the initial perturbation propagation. The same concerns the amplification of waves with different frequencies for fixed parameters of the plasma; i.e., the difference between the amplification coefficients is larger, the lower the wave frequency. The resultant analytic dependences make it possible to determine exactly which of the problems (with the initial or boundary conditions) should be solved to compute the amplification coefficient of acoustic waves under specific experimental conditions.