  We consider propagation of high-frequency wave packets along a smooth
evolving background flow whose evolution is described by a simple-wave type of
solutions of hydrodynamic equations. In geometrical optics approximation, the
motion of the wave packet obeys the Hamilton equations with the dispersion law
playing the role of the Hamiltonian. This Hamiltonian depends also on the
amplitude of the background flow obeying the Hopf-like equation for the simple
wave. The combined system of Hamilton and Hopf equations can be reduced to a
single ordinary differential equation whose solution determines the value of
the background amplitude at the location of the wave packet. This approach
extends the results obtained in Ref.~\cite{ceh-19} for the rarefaction
background flow to arbitrary simple-wave type background flows. The theory is
illustrated by its application to waves obeying the KdV equation.
