The sixth-order wave equation governing the propagation of one-dimensional acoustic waves in a viscous, heat conducting gaseous medium subject to relaxation effects has been considered. It has been reduced to a system of lower order equations corresponding to the finite speeds occurring in the equation, following a method due to Whitham. The lower order equations are much simpler and easier to solve than the original equation. As an illustration, the problem of harmonic wave propagation due to oscillations of a planar wall has been considered, and analytical expressions for the damping coefficients and wave speeds have been obtained.