Brillouin spectra of glycerol measured in the visible, ultraviolet and X-ray frequency regions allow us to reckon the imaginary part of acoustic compliance, J″( ω), over a broad frequency range from fraction of GHz to tens of THz. We observe that J″( ω) suitably mimic the shape of the tagged particle susceptibility, χ″ INS ( ω), measured by incoherent neutron spectra for both the liquid and supercooled states. The proportionality between these two quantities suggests a strict relationship between acoustic dissipation and generalized density of states.