It is shown that a gravitationally bound system with a one-dimensional velocity dispersion \sigma can at most dissipate a fraction \sim 36 ( \sigma / c ) ^ { 3 } of the gravitational wave energy propagating through it , even if their dynamical time is shorter than the wave period . The limit is saturated for low frequency waves propagating through a system of particles with a mean-free-path equal to the size of the system , such as hot protons in galaxy clusters , strongly-interacting dark matter particles in halos , or massive black holes in clusters . For such systems with random motions and no resonances , the dissipated fraction , \lesssim 10 ^ { -6 } , does not degrade the use of gravitational waves as cosmological probes . At high wave frequencies , the dissipated fraction is additionally suppressed by the square of the ratio between the collision frequency and the wave frequency . The electromagnetic counterparts that result from the dissipation are too faint to be detectable at cosmological distances .