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The combined observation of GW170817 and its electromagnetic counterpartGRB170817A reveals that gravitational waves propagate at the speed of light inhigh precision. We apply the effective field theory approach to investigate theexperimental consequences for the theory of $f(T)$ gravity. We find that thespeed of gravitational waves within $f(T)$ gravity is exactly equal to thelight speed, and hence the constraints from GW170817 and GRB170817A aretrivially satisfied. The results are verified through the standard analysis ofcosmological perturbations. Nevertheless, by examining the dispersion relationand the frequency of cosmological gravitational waves, we observe a deviationfrom the results of General Relativity, quantified by a new parameter. Althoughits value is relatively small in viable $f(T)$ models, its possible futuremeasurement in advancing gravitational-wave astronomy would be the smoking gunof testing this type of modified gravity.

$f(T)$ gravity after GW170817 and GRB170817A