  This paper complements the study of the wave equation with discontinuous
coefficients initiated in \cite{DGL:22} in the case of time-dependent
coefficients. Here we assume that the equation coefficients are depending on
space only and we formulate Levi conditions on the lower order terms to
guarantee the existence of a very weak solution as defined in \cite{GR:14}. As
a toy model we study the wave equation in conservative form with discontinuous
velocity and we provide a qualitative analysis of the corresponding very weak
solution via numerical methods.
