  Whole excitation spectrum is calculated within the Popov approximation of the
Bogoliubov theory for a cylindrical symmetric Bose-Einstein gas trapped
radially by a harmonic potential. The full dispersion relation and its
temperature dependence of the zero sound mode propagating along the axial
direction are evaluated in a self-consistent manner. The sound velocity is
shown to depend not only on the peak density, but also on the axial area
density. Recent sound velocity experiment on Na atom gas is discussed in light
of the present theory.
