We show that the gravitational wave source counts distribution can test how
gravitational radiation propagates on cosmological scales. This test does not
require obtaining redshifts for the sources. If the signal-to-noise from a
gravitational wave source is proportional to the strain then it falls as
$R^{-1}$, thus we expect the source counts to follow $dN/dS \propto S^{-4}$.
However, if gravitational waves decay as they propagate or can propagate into
other dimensions, then there can be deviations from this generic prediction. We
consider the possibility that the signal-to-noise falls as $R^{-\gamma}$, where
$\gamma=1$ recovers the expected predictions in a Euclidean uniformly-filled
universe. We forecast the sensitivity of future observations in constraining
gravitational wave physics using this method by simulating sources distributed
over a finite range of signal-to-noise. We first consider the case of few
objects, 7 sources, with a signal-to-noise from 8 to 24, and impose a lower
limit on $\gamma$, finding $\gamma>0.33$ at 95% confidence level. The
distribution of our simulated sample is very consistent with the distribution
of the candidate black holes binary systems observed by Advanced LIGO. We then
consider the improvement coming from further detections, simulating 100
observations spanning a wider range of signal-to-noise and measure $\gamma$
with $\sigma(\gamma)\sim 0.15$, percent level precision will be possible with
10000 objects. We generalize the formalism to account for a range of chirp
masses and the possibility that the signal falls as $\exp(-R/R_0)/R^\gamma$.