  We investigate the first sound of a normal dilute and ultracold two-component
Fermi gas in a harmonic microtube, i.e. a cylinder with harmonic transverse
radial confinement in the length-scale of microns. We show that the velocity of
the sound that propagates along the axial direction strongly depends on the
dimensionality of the system. In particular, we predict that the first-sound
velocity display shell effects: by increasing the density, that is by inducing
the crossover from one-dimension 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 40K
atoms.
