  A formalism is introduced which may describe both standard linearized waves
and gravitational waves in Isaacson's high-frequency limit. After emphasizing
main differences between the two approximation techniques we generalize the
Isaacson method to non-vacuum spacetimes. Then we present three large explicit
classes of solutions for high-frequency gravitational waves in particular
backgrounds. These involve non-expanding (plane, spherical or hyperboloidal),
cylindrical, and expanding (spherical) waves propagating in various universes
which may contain a cosmological constant and electromagnetic field. Relations
of high-frequency gravitational perturbations of these types to corresponding
exact radiative spacetimes are described.
