The sound attenuation in the THz region is studied down to T=16 K in glassy glycerol by inelastic x-ray scattering. At striking variance with the decrease found below 100 K in the GHz data, the attenuation in the THz range does not show any T dependence. This result i) indicates the presence of two different attenuation mechanisms, active respectively in the high and low frequency limits; ii) demonstrates the non-dynamic origin of the attenuation of THz sound waves, and confirms a similar conclusion obtained in SiO2 glass by molecular dynamics; and iii) supports the low frequency attenuation mechanism proposed by Fabian and Allen (Phys.Rev.Lett. 82, 1478 (1999)).