  The present work investigates some exact solutions of the gravitational wave
equation in some widely used cosmological spacetimes. The examples are taken
from spatially flat and closed isotropic models as well as Kasner metric which
is anisotropic. Various matter distributions are considered, from the standard
dust or radiation distribution to exotic matters like that with an equation of
state $P = - \frac{1}{3} \rho$. In almost all cases the frequency and amplitude
of the wave are found to be decaying with evolution, except for a closed
radiation universe where there is a resurgence of the waveform, consistent with
the recollapse of the universe into the big crunch singularity.
