The velocity of fast and slow collective modes of 90, 94 and 98% porosity aerogels filled with superfluid helium were measured by means of low-frequency resonant technique at temperatures 0.5-2.5 K. The temperature dependences of velocities of both modes are compared with the hydrodynamic theory which was modified taking into account the mobility of the aerogel matrix, porosity of media and tortuosity of an acoustic way. It has been found that the fast and slow modes in an aerogel are coupled much stronger than the first and second sounds in bulk He II.

The dynamical equations for superfluid He–A3 filled aerogel in finite magnetic fields are determined. The speeds of propagating longitudinal modes in the A1 and A phases of this system are found. It is shown that sound phenomena in the case of He–A13 superfluid are modified from those for HeII superfluid.

A theory of the propagation of acoustic waves in a porous medium filled with superfluid helium is developed. The elastic coefficients in the system of equations are expressed in terms of physically measurable quantities. The equations obtained describe all volume modes which propagate in a porous medium saturated with superfluid helium. The propagation velocities of longitudinal and transverse waves are calculated in the limit of high and low oscillation frequencies of the thermodynamic quantities.

A theory of the propagation of acoustic waves in a porous medium filled with superfluid 3He–4He solution is developed. The elastic coefficients in the system of equations are expressed in terms of physically measurable quantities. The equations obtained describe all volume modes that can propagate in a porous medium saturated with superfluid 3He–4He solution. Finally, derived equations are applied to the most important particular cases when the normal fluid component is locked inside a highly porous medium (aerogel) by viscous forces. The velocities of two longitudinal sound and transverse modes are calculated.

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