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

more »

... d of sound in both the BCS and the unitary regime differs by a factor sqrt3/5 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.