  We evaluate the transition from zero-sound to first-sound behaviour with
increasing collisionality in the propagation of density waves through an
ultracold gaseous mixture of fermionic atoms confined in the normal state
inside a cigar-shaped harmonic trap. We study for this purpose the evolution of
the one-body distribution functions associated with a density perturbation
generated in the central region of the cloud, as obtained by solving
numerically the Vlasov-Landau equations. We examine a variety of trap
anisotropies and of repulsive or attractive interaction strengths between the
components of the mixture, and the speed of propagation of the density
disturbance is found to decrease in both cases as the magnitude of the coupling
strength is increased. The results are compared with the values of the speed of
zero sound and of first sound, as obtained analytically from the limit of
vanishing collisionality and from linearized hydrodynamics. The main effects of
the quasi-one-dimensional confinement are the stabilization of zero-sound
excitations in the attractive regime before collapse and the lowering of the
hydrodynamic sound velocity by a factor \sqrt{3/5} relative to
three-dimensional behaviour.
