Аннотация:A variant of the Cauchy formalism is introduced that allows constructing closed-form solutions of the equations of motion for harmonic acoustic waves propagating in a functionally graded (FG) rod with arbitrary longitudinal inhomogeneity. The explicit solutions are derived for exponential, polynomial and periodic inhomogeneities. The constructed solutions revealed some interesting phenomena related to the variation of strain and kinetic energy of the wave in the case of a periodic inhomogeneity.