Suppression of gravitational radiation

We consider a burst of quadrupole gravitational radiation in the presence of a large static mass situated at its source. Some of the radiation is back-scattered off the static field of the large mass, forming a wave tail. After the burst, the tail is a pure incoming wave, carrying energy back towards the source. We calculate this energy, and, in a numerical example, compare it with the outgoing wave energy. Under certain conditions the incoming energy can be a noticeable fraction of the outgoing energy, causing a partial suppression of the emission. It is argued that the tails should be carefully considered in energy calculations on outgoing waves.