We study low-energy collective excitations in a trapped superfluid Fermi gas. These excitations originate from slow variations of the phase of the superfluid order parameter and, in this sense, are similar to the Bogolyubov sound in a homogeneous superfluid Fermi gas. Well below the critical temperature the eigenfrequencies of the lowest collective excitations are of the order of the trap frequency, and these modes manifest themselves in the density oscillations under periodic modulations of the trap frequencies. This gives a clear signature of the presence of a superfluid phase.