  We study the Bogoliubov spectrum of an elongated Fermi superfluid confined in
an one-dimensional superfluid along the Bose-Einstein-condensate
(BEC)-Bardeen-Cooper-Schrieffer (BCS) crossover. We derive analytic expressions
for the sound velocity, effective mass and the Bogoliubov excitation spectrum
of the axial quasiparticles long the crossover based on the hydrodynamic
theory. Our investigation reveal interesting signatures of BEC-BCS crossover in
an optical lattice which deserve experimental investigation.
