Sound velocities in fluid and crystalline hydrogen were measured under pressure to 24 gigapascals by Brillouin spectroscopy in the diamond anvil cell. The results provide constraints on the intermolecular interactions of dense hydrogen and are used to construct an intermolecular potential consistent with all available data. Fluid perturbation theory calculations with the potential indicate that sound velocities in hydrogen at conditions of the molecular layer of the Jovian planets are lower than previously believed. Jovian models consistent with the present results remain discrepant with recent free oscillation spectra of the planet by 15 percent. The effect of changing interior temperatures, the metallic phase transition depth, and the fraction of high atomic number material on Jovian oscillation frequencies is also investigated with the Brillouin equation of state. The present data place strong constraints on sound velocities in the Jovian molecular layer and provide an improved basis for interpreting possible Jovian oscillations.