One-dimensional acceleration waves in granular materials were investigated by J. W. Nunziato and K. Walsh (1.) Their work is based on the theory of granular materials derived by Cowin and Goodman in papers (2, 3, 4.) J. W. Nunziato and K. Walsh investigated the properties of one-dimensional acceleration waves in materials with non-uniform initial looseness of the particles of the granular skeleton. In this paper, we consider the properties of acceleration waves from the most general point of view in the case of thermally conductive granular materials. Considering the complexity and extent of this problem, the case of the absence of thermal effects is considered separately. It is shown that in such materials there are three acoustic waves which, in the general case, do not have to be either transverse or longitudinal. Further, special cases are analyzed and the values of the speed of wave propagation are shown. Special interest is shown in the influence of the arrangement and interconnection of voids in granular materials on wave propagation.