This work outlines a mathematical model of the pressure wave propagation in the gas media containing different liquid particles such as water droplets and offers the method to estimate the influence of the energy exchange between phases on the evolution of the wave under different conditions of the interphase interactions. Conservation equations describing the propagation and structure of finite amplitude perturbations in such a medium, with correction for heat transfer and momentum exchange between the phases have been employed to obtain an evolution of the wave profile during of the pressure wave propagation. Such a media is dispersive due to the finite rate of the above exchange processes. The resultant equations in general incorporate integral terms containing the amplitude of the perturbation. The derived equations are capable of describing the evolution of waves at any ratio between time of the internal process and the characteristic period of the pressure wave. The solutions can be used for determining the dissipation of energy of a wave passing through a medium containing liquid droplets. The proposed approach neglects the effect of droplets' temperature influence on the gas bulk. Two extreme cases have been considered, one for long-wave and the other one for short-wave interaction. Final results show that there are analytical solutions for some of the specific cases of the interaction between phases. The finding could be used for estimation of wave dissipation in medium containing different liquid particles.