We use hydrodynamic equations to study sound propagation in a superfluid
Fermi gas inside a strongly elongated cigar-shaped trap, with main attention to
the transition from the BCS to the unitary regime. We treat first the role of
the radial density profile in the quasi-onedimensional limit and then evaluate
numerically the effect of the axial confinement in a configuration in which a
hole is present in the gas density at the center of the trap. We find that in a
strongly elongated trap the speed of sound in both the BCS and the unitary
regime differs by a factor sqrt{3/5} from that in a homogeneous
three-dimensional superfluid. The predictions of the theory could be tested by
measurements of sound-wave propagation in a set-up such as that exploited by
M.R. Andrews et al. [Phys. Rev. Lett. 79, 553 (1997)] for an atomic
Bose-Einstein condensate
