  We study the propagation of sound waves in a Bose-Einstein condensate trapped
in a one-dimensional optical lattice. We find that the velocity of propagation
of sound wavepackets decreases with increasing optical lattice depth, as
predicted by the Bogoliubov theory. The strong interplay between nonlinearities
and the periodicity of the external potential raise new phenomena which are not
present in the uniform case. Shock waves, for instance, can propagate slower
than sound waves, due to the negative curvature of the dispersion relation.
Moreover, nonlinear corrections to the Bogoliubov theory appear to be important
even with very small density perturbations, inducing a saturation on the
amplitude of the sound signal.
