  The nonasymptotic critical behavior of sound attenuation coefficient has been
studied in an elastically isotropic Ising system above the critical point on
the basis of a complete stochastic model including both spin-energy and
lattice-energy modes linearly coupled to the longitudinal sound mode. The
effect of spin-lattice relaxation on the ultrasonic attenuation is
investigated. The crossover between weak-singularity behavior $t^{-2 \alpha}$
and strong singularity behavior $t^{-(z \nu +\alpha)}$ is studied. A new
high-frequency regime with singularity of the type $t^{-z \nu +\alpha}$ is
discovered in the magnetic systems. This new regime corresponds to an adiabatic
sound propagation and is very similar to the ones in binary mixture and liquid
helium. A new frequency-dependent specific-heat being the harmonic average of
the bare lattice and critical spin specific-heats is introduced. It was shown
that such specific-heat descibes the process of equilibrization between spin
and lattice subsystems and includes the most important features of critical
sound attenuation. In some regions of coupling constants the acoustic
self-energy can be very well approximated solely by this quantity.
