  We study the effect of the transverse degrees of freedom on the velocity of
sound in a Bose-Einstein condensate immersed in a one-dimensional optical
lattice and radially confined by a harmonic trap. We compare the results of
full three-dimensional calculations with those of an effective 1D model based
on the equation of state of the condensate. The perfect agreement between the
two approaches is demonstrated for several optical lattice depths and
throughout the full crossover from the 1D mean-field to the Thomas Fermi regime
in the radial direction.
