  We study the zero sound and the first sound in a dilute and ultracold
disk-shaped normal Fermi gas with a strong harmonic confinement along the axial
direction and uniform in the two planar directions. Working at zero temperature
we calculate the chemical potential $\mu$ of the fermionic fluid as a function
of the uniform planar density $\rho$ and find that $\mu$ changes its slope in
correspondence to the filling of harmonic axial modes (shell effects). Within
the linear response theory, and under the random phase approximation, we
calculate the velocity $c^{0}_s$ of the zero sound. We find that also $c^0_s$
changes its slope in correspondence of the filling of the harmonic axial modes
and that this effect depends on the Fermi-Fermi scattering length $a_F$. In the
collisional regime, we calculate the velocity $c_s$ of first sound showing that
$c_s$ displays jumps at critical densities fixed by the scattering length
$a_F$. Finally, we discuss the experimental achievability of these zero sound
and first sound waves with ultracold alkali-metal atoms.
