Sound attenuation coefficient is calculated for a spin-1 Ising system on the basis of Onsager theory of irreversible processes and its behaviour near the second-order phase transition point or the critical point is analyzed according to various values of Onsager or phenomenological rate coefficients (gamma (ij)). For all gamma (S) and gamma (Q) values it is observed that the sound attenuation peaks occur below T-C and depend on frequency (omega) and on the value of the off-diagonal Onsager coefficient (gamma). On the other hand, in the hydrodynamic regime the attenuation converges to zero with a mean field exponent (lambda = 1.0) just below the transition, while it vanishes above the critical temperature and then remains temperature-independent. Moreover, the behaviour of the sound attenuation as a function of frequency is also investigated and omega (2) dependence is observed for the attenuation coefficient. These results are in a good agreement with ultrasonic investigations of some magnetic systems, such as MnF2, qFeF(2), and RbMnF3. (C) 2001 Elsevier Science B.V. All rights reserved.