  Within the closed universe, we obtain the amplitude and frequency of
gravitational waves in the terms of discrete wave numbers, wave propagation
time, and cosmological constant using the deviation equation in the first-order
perturbed metric. We demonstrate that the cosmological constant effect on GWs
is only seen in the early universe. Also, by considering the time evolution of
a gravitational wave in a closed spacetime, we investigate its effect on a
circle of nearby massless particles, which will be compared with this case in
the flat spacetime. Expanding the universe has effective damping on GWs; thus,
we suggest it can be used as a tool to characterize the large-scale curvature
of the universe
