Brillouin scattering spectra of water from T = 30 degrees C down to supercooling temperatures of about T = -26 degrees C have been measured, at different scattering angles and for different exciting wavelengths, covering exchanged wave vector values from 0.0137 to 0.0351 nm(-1). A fit of the spectra using the hydrodynamic line shape for a simple fluid confirms the existence of a relevant dispersion in the wave vector dependence of the hypersonic sound velocity. The parameters obtained fitting the data with a relaxing hydrodynamic model indicate the ratio between volume and shear viscosity is almost temperature independent also in the supercooled regime and that a single relaxation process, involving almost entirely both shear and volume viscosities, accounts for the observed dispersion. The infinite frequency sound velocity is found to be of about 2150 m/s almost independently on temperature. The temperature dependence of the relaxation time is discussed and compared with that of other relaxation times available in the literature. Predictions are made for the temperature and wave vector values at which the dispersion of sound velocity should be best observed.