We investigate the first sound of a normal dilute and ultracold two-component Fermi gas in a cylindrical trap with harmonic radial confinement. We show that the velocity of the sound that propagates along the axial direction strongly varies in the dimensional crossover of the system. In particular, we predict that the first-sound velocity exhibits shell effects: by increasing the density, that is by inducing the crossover from one to three-dimensions, the first-sound velocity shows jumps in correspondence with the filling of harmonic modes. The experimental achievability of these effects is discussed by considering K-40 atoms.
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