  It has been shown in the literature that detections of gravitational waves
(GWs) emitted by binary sources can provide measurements of luminosity
distance. The events followed by electromagnetic counterparts are, then,
suitable for probing the distance-redshift relation and doing cosmological
parameter estimation, as well as investigating modified gravity (MG) models. In
the context of effective approaches to MG equivalent to Horndeski, this GW
distance differs from the standard electromagnetic luminosity distance due to
the presence of a modified friction in the wave propagation. Here, we
investigate how precisely the future-planned interferometer Einstein Telescope
will probe such deviations from General Relativity, considering
phenomenological parametrizations for both the dark energy equation of state
and the GW friction. Despite being an independent test of gravity, for $f(R)$
in particular, we conclude that it may provide weaker constraints than the
current available ones.
