Acoustical activity of isomorphous crystals Bi12GeO20 and Bi12SiO20 has been studied by measuring the splitting of degeneracy of transverse acoustical waves propagating along high symmetric direction with inelastic neutron scattering. One of the interesting results is that the left and right circularly polarized modes of acoustical phonons propagating along direction are subjected to different attenuation. This conclusion is verified by both kinds of crystals. The experimental result is observed for the first time in the study of acoustical activity. The life-time of the phonon with larger attenuation is found to be about 2×10-11 s. experimentally.