The paper presents one-dimensional problems of dusty gas dynamics on plane acoustic wave propagation. In the fist problem the dusty gas is considered as polydisperse medium with a zero-volume dust fraction. In the second problem the dusty gas is a monodisperse medium with particles that occupy finite volume. For both problems, dispersion relations are obtained. Then a limiting case when a velocity relaxation time between particles and gas tends to zero is considered. This case corresponds to mixtures with fine dust when intense interaction between phases takes place. For this limiting case expressions for the phase velocity are derived. Moreover, we present formulas for generating particular solutions of corresponding linearized problems. These solutions are intended to be used as a standard in the study of asymptotic, dispersive and dissipative properties of numerical methods. Program codes for generating such solutions are published and available for download.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.