  We investigate the superfluid properties of a Bose-Einstein condensate (BEC)
trapped in a one dimensional periodic potential. We study, both analytically
(in the tight binding limit) and numerically, the Bloch chemical potential, the
Bloch energy and the Bogoliubov dispersion relation, and we introduce {\it two}
different, density dependent, effective masses and group velocities. The
Bogoliubov spectrum predicts the existence of sound waves, and the arising of
energetic and dynamical instabilities at critical values of the BEC
quasi-momentum which dramatically affect its coherence properties. We
investigate the dependence of the dipole and Bloch oscillation frequencies in
terms of an effective mass averaged over the density of the condensate. We
illustrate our results with several animations obtained solving numerically the
time-dependent Gross-Pitaevskii equation.
