  We study the collective modes of a confined gaseous cloud of bosons and
fermions with mutual attractive interactions at zero temperature. The cloud
consists of a Bose-Einstein condensate and a spin-polarized Fermi gas inside a
spherical harmonic trap and the coupling between the two species is varied by
increasing either the magnitude of the interspecies s-wave scattering length or
the number of bosons. The mode frequencies are obtained in the collisional
regime by solving the equations of generalized hydrodynamics and are compared
with the spectra calculated in the collisionless regime within a random-phase
approximation. We find that, as the mixture is driven towards the collapse
instability, the frequencies of the modes of fermionic origin show a blue shift
which can become very significant for large numbers of bosons. Instead the
modes of bosonic origin show a softening, which becomes most pronounced in the
very proximity of collapse. Explicit illustrations of these trends are given
for the monopolar spectra, but similar trends are found for the dipolar and
quadrupolar spectra except for the surface (n=0) modes which are essentially
unaffected by the interactions.
