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We consider the temperature dependence of the sound attenuation and soundvelocity in layered impure metals due to superconducting fluctuations of theorder parameter above the critical temperature. We obtain the dependence onmaterial properties of these fluctuation corrections in the hydrodynamic limit,where the electron mean free path is much smaller than the wavelength of soundand where the electron collision rate is much larger than the sound frequency.For longitudinal sound propagating perpendicular to the layers, the open Fermisurface condition leads to a suppression of the divergent contributions toleading order, in contrast with the case of paraconductivity. The leadingtemperature dependent corrections, given by the Aslamazov-Larkin, Maki-Thompsonand density of states terms, remain finite as T->Tc. Nevertheless, thesensitivity of new ultrasonic experiments on layered organic conductors shouldmake these fluctuations effects measurable.Comment: 13 pages, 6 figures. Accepted for PRB. Added discussion on incoherent  interlayer tunneling and other small modifications suggested by referee

Superconducting fluctuation corrections to ultrasound attenuation in layered superconductors