Experimental and simulation studies of sound propagation in water have observed, at large wave vectors k (k > 0.25 Angstrom(-1)), a longitudinal sound mode with a velocity of about 3500 m/s, more than twice the hydrodynamic sound velocity. The relation between the hydrodynamic sound mode and the high frequency mode has been the center of contrasting interpretations. In this paper, we report extensive molecular dynamics simulations designed ad hoc to explore the intermediate and low k part of the collective spectrum. We calculate the dispersion relations for longitudinal and transverse collective modes from 0.026 to 1 Angstrom(-1) for a range of temperatures. At all temperatures studied, the sound velocity increases with k. At the highest studied temperature, the sound velocity changes from values comparable to hydrodynamic sound velocity to ones observed by neutron scattering experiments. We show that the viscoelastic approximation describes the data satisfactorily. We also perform normal mode analysis of quenched liquid configurations to obtain further information about the behavior observed at intermediate frequencies (50-100 cm(-1)). We find further positive dispersion of the sound branch at these frequencies and indications which suggest the interaction of the sound branch with localized modes as the origin of such dispersion.