  An effective Hamiltonian for the Bose subsystem in the mixture of ultracold
atomic clouds of bosons and fermions with mutual attractive interaction is used
for investigating collective excitation spectrum. The ground state and mode
frequencies of the $^{87}$Rb and $^{40}$K mixture are analyzed quantitatively
at zero temperature. We find analytically solutions of the hydrodynamics
equations in the Thomas- Fermi approximation. We discuss the relation between
the onset of collapse and collective modes softening and the dependence of
collective oscillations on scattering length and number of boson atoms.
