  We consider a model of nonlinear wave equations with periodically varying
wave speed and periodic external forcing. By imposing non-resonance conditions
on the frequency, we establish the existence of the response solutions (i.e.,
periodic solutions with the same frequency as the forcing) for such a model in
a Cantor set of asymptotically full measure. The proof relies on a
Lyapunov--Schmidt reduction together with the Nash--Moser iteration.
