  We study the production of gravitational waves by a thermalized plasma of
$\mathcal N$=4 Supersymmetric Yang Mills matter. We focus on the large number
of colors limit, $N_c\rightarrow \infty$, and compute the spectrum of
gravitational waves both for infinitely large and infinitesimally small values
of the 't Hooft coupling constant $\lambda$. In the $\lambda\rightarrow \infty$
limit we employ the gauge/gravity duality to compute the emission rate via the
analysis of Energy-Momentum tensor thermal correlators. In the $\lambda
\rightarrow 0$ limit we employ state-of-the-art perturbative analyses to
calculate the complete leading order emission rate. By comparing these extreme
limits, we bracket the magnitude of the spectrum induced by this source of
gravitational waves. Embedding our results in a cosmological evolution model,
we find qualitative and quantitative similarities between the strong coupling
spectrum and the extrapolation of the perturbative results up to an
intermediate value of the coupling, after an appropriate re-scaling of the
effective number of degrees of freedom. We comment on how our results can help
better understand the contribution of thermalized matter to the stochastic
spectrum of gravitational waves.
