  This paper is concerned with the periodic (in time) solutions to an
one-dimensional semilinear wave equation with $x$-dependent coefficient. Such a
model arises from the forced vibrations of a nonhomogeneous string and
propagation of seismic waves in nonisotropic media. By combining variational
methods with saddle point reduction technique, we obtain the existence of at
least three periodic solutions whenever the period is a rational multiple of
the length of the spatial interval. Our method is based on a delicate analysis
for the asymptotic character of the spectrum of the wave operator with
$x$-dependent coefficients, and the spectral properties play an essential role
in the proof.
