  The problem studied in this paper is to obtain the equations describing sound
propagation in a consolidated porous medium filled with superfluid, determine
the elastic coefficients, appearing in the equations, in terms of physically
measurable quantities, and calculate the propagation velocities of transverse
and longitudinal waves at high and low oscillating frequencies. In general, the
obtained equations describe all volume modes that can propagate in a porous
medium saturated with superfluid for any values of the porosity and
frequencies. The derived equations are applied to the most important particular
case when the normal component of superfluid helium is locked inside a highly
porous media (aerogel, Im-helium sample) by viscous forces. For this case the
velocities of two longitudinal sound modes and transverse mode are calculated
from the derived equations. There are established the coupling between
temperature and pressure oscillations in these fast and slow modes.
