A low threshold acoustic cavitation regime was observed for the excitation of hypersonic waves due to a stimulated Brillouin scattering (SBS) mechanism, when the optical pump lies within the uv frequency range. Cavitation occurs if the optical pump bandwidth Delta(+)>>Omega(0), where Omega(0) is the Stokes frequency shift (the hypersonic frequency). In the opposite case (Delta(+)<<Omega(0)), cavitation does not occur despite the fact that the hypersonic wave intensity is much higher. The effect is associated with the stimulation of a broad frequency spectrum of hypersonic pressure in a field provided by the broadband optical pump. In contrast, for a monochromatic optical pump, the hypersonic wave is of single-frequency character. Induction of cavitation at the low intensities of acoustic pressure is attributed to nanobubbles of fixed size that occur in the liquid. The resonant frequency of the nanobubbles coincides with the frequency of some spectral component of hypersound present in the broadband SBS process. That conclusion is reinforced by the further observation that at the same intensity of broadband pumping the cavitation vanishes after degassing the liquid. In parallel experiments on four-photon polarization Rayleigh wing spectroscopy, it was also demonstrated that spectral lines exist in ordinary (not degassed) water, which can be ascribed to resonances of radial vibrations of nanobubbles. Those lines are absent in the degassed water spectrum.