This paper is devoted to the study of the interaction of particles with two beating plasma waves. We follow the instructional article by Ott and Dum. According to them, the sum of wave actions during the interaction is constant, supposing the effect of trapped particles on the beat can be neglected. In the present paper, this problem is solved more generally, just for the case of trapped and also untrapped particles in the wave. Our study shows that the sum of wave actions is constant also in the case when the influence of the trapped particles on the amplitudes of two waves was considered. On the contrary this conclusion is not valid if it is supposed that two original waves are amplitude modulated e.g. by the influence of the interaction of the beat with particles.