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

Sound propagation in elongated superfluid fermionic clouds