Abstract: The propagation characteristics of waves are the basis for studying the dynamic behavior of materials, and the study of continuous medium wave theory at the macro scale is quite comprehensive. With the in-depth application of materials and structures at the micro and nano scales, research on the wave characteristics at the lattice scale is receiving increasing attention. In this article, the Tersoff potential interaction between lattices is applied to study the wave propagation characteristics in single lattice systems and polycrystalline systems, respectively. Firstly, in the case of micro vibrations, the propagation of lattice waves in a single lattice system was studied based on three conditions: linear interaction, Tersoff potential, and Tersoff potential with defects between lattices. The relationship between lattice wave velocity and angular frequency was obtained. Secondly, taking carbon and silicon lattices as examples, the finite difference method was applied to study the wave propagation process in a single lattice system under three different potentials, and the influence of incident velocity on displacement peak and force peak was discussed, revealing the difference in wave propagation between a single lattice system and a continuous medium. Finally, taking diamond and silicon carbide as examples, molecular dynamics simulations were used to study the wave propagation characteristics in polycrystalline systems. The results indicate that the wave propagation characteristics in polycrystalline systems are different from those in single lattice systems, and the presence of defects has a significant impact on the wave propagation. This study has good reference significance for the study of material dynamics performance at micro and nano scales.