By applying a new two-step line-shape analysis to inelastic neutron and x-ray scattering spectra of glassy systems, we were able to resolve the acoustic excitations from the low-frequency excess modes and to accurately estimate the damping of sound waves in the terahertz frequency range. Using this approach, we estimated the damping parameter for terahertz acoustic waves in a wide class of chemically different glasses and did a quantitative comparison of the results with prediction of theoretical models. By comparing the estimates of the mean-free path of the acoustic modes in different glasses and the corresponding boson peak strengths, we show the existence of a simple correlation between these two quantities. The relationship between attenuation of the terahertz acoustic modes, strength of the boson peak, and fragility is discussed.