  We consider sound waves in superfluid nucleon-hyperon matter of massive
neutron-star cores. We calculate and analyze the speeds of sound modes and
their damping times due to the shear viscosity and non-equilibrium weak
processes of particle transformations. For that, we employ the dissipative
relativistic hydrodynamics of a superfluid nucleon-hyperon mixture, formulated
recently [M.E. Gusakov and E.M. Kantor, Phys. Rev. D78, 083006 (2008)]. We
demonstrate that the damping times of sound modes calculated using this
hydrodynamics and the ordinary (nonsuperfluid) one, can differ from each other
by several orders of magnitude.
