Combined Brillouin spectra collected at visible, ultraviolet, and x-ray frequencies are used to reconstruct the imaginary part of the acoustic compliance J'' over a wide frequency range between 0.5 GHz and 5 THz. For liquid, supercooled, and glassy glycerol, J'' is found to be linearly dependent on the tagged-particle susceptibility measured by incoherent neutron scattering up to ≃1 THz, giving evidence of a clear relation between acoustic power dissipation and density of states. A simple but general formalism is presented to quantitatively explain this relation, thus clarifying the connection between the quasielastic component observed in neutron scattering experiments and the fast relaxation dynamics probed by Brillouin scattering.