  By taking the hydrodynamic limit we derive, at $T=0$, an explicit solution of
the linearized time dependent Gross-Pitaevskii equation for the order parameter
of a Bose gas confined in a harmonic trap and interacting with repulsive
forces. The dispersion law $\omega=\omega_0(2n^2+2n\ell+3n+\ell)^{1/2}$ for the
elementary excitations is obtained, to be compared with the prediction
$\omega=\omega_0(2n+\ell)$ of the noninteracting harmonic oscillator model.
Here $n$ is the number of radial nodes and $\ell$ is the orbital angular
momentum. The effects of the kinetic energy pressure, neglected in the
hydrodynamic approximation, are estimated using a sum rule approach. Results
are also presented for deformed traps and attractive forces.
