The equation for the energy density of a longitudinal wave in a thin rod is
$$w = \rho\cdot \left(\frac{\partial \xi}{\partial t}\right)^2$$
So the energy density seems to be 0 when the deviation ($\xi$) is maximal.
I don't understand how this can be true: if $\xi$ is big, this means that there must be big potential energy, since we have done the work of increasing $\xi$.