The sound attenuation phenomena is investigated for a spin-3/2 Ising model on the Bethe lattice in terms of the recursion relations by using the Onsager theory of irreversible thermodynamics. The dependencies of sound attenuation on the temperature (T), frequency (omega), Onsager coefficient (gamma) and external magnetic field (H) near the second-order (T-c) and first-order (T-t) phase transition temperatures are examined for given coordination numbers q on the Bethe lattice. It is assumed that the sound wave couples to the order-parameter fluctuations which decay mainly via the order-parameter relaxation process, thus two relaxation times are obtained and which are used to obtain an expression for the sound attenuation coefficient (alpha). Our investigations revealed that only one peak is obtained near T-t and three peaks are found near T-c when the Onsager coefficient is varied at a given constant frequency for q = 3. Fixing the Onsager coefficient and varying the frequency always leads to two peaks for q = 3, 4 and 6 near T-c. The sound attenuation peaks are observed near T-t at lower values of external magnetic field, but as it increases the sound attenuation peaks decrease and eventually disappear. (C) 2012 Elsevier B.V. All rights reserved.