The temperature (T), frequency (w), Onsager coefficient (gamma) and external magnetic field (H) dependencies of the sound attenuation near the phase transition temperature (T-c) is studied for the spin-1 Ising model on the Bethe lattice for given coordination numbers q in terms of the recursion relations by using Onsager theory of irreversible thermodynamics. It was assumed that the sound wave couples to the order-parameter fluctuations which decay mainly via the order-parameter relaxation process. Two relaxation times are obtained and which are used to find an expression for the sound attenuation coefficient (alpha). It was found that alpha presents only one peak for all frequencies when q = 6, and two peaks for q = 3 and 4 at low frequencies. In addition, alpha increases with the increasing values of frequency and with the decreasing values of external magnetic field.