  We carry out a detailed analysis of the short-wave (semiclassical)
approximation for the linear equations of the elasticity in a smoothly
inhomogeneous isotropic medium. It is shown that the polarization properties of
the transverse waves are completely analogous to those of electromagnetic waves
and can be considered as spin properties of optical phonons. In particular, the
Hamiltonian of the transverse waves contains an additional term of the phonon
spin-orbit interaction arising from the Berry gauge potential in the momentum
space. This potential is diagonal in the basis of the circularly polarized
waves and corresponds to the field of two `magnetic monopoles' of opposite
signs for phonons of opposite helicities. This leads to the appearance of the
Berry phase in the equation for the polarization evolution and an additional
``anomalous velocity'' term in the ray equations. The anomalous velocity has
the form of the `Lorentz force' caused by the Berry gauge field in momentum
space and gives rise to the transverse transport of waves of opposite
helicities in opposite directions. This is a manifestation of the spin Hall
effect of optical phonons. The effect directly relates to the conservation of
total angular momentum of phonons and also influences reflection from a sharp
boundary (acoustic analogue of the transverse Ferdorov--Imbert shift).
