  Interferometric gravitational wave detectors are dynamic instruments.
Changing gravitational-wave strains influence the trajectories of null
geodesics and therefore modify the interferometric response. These effects will
be important when the associated frequencies are comparable to the round-trip
light travel time down the detector arms. The arms of advanced detectors
currently in operation are short enough that the strain can be approximated as
static, but planned 3$^\mathrm{rd}$ generation detectors, with arms an order of
magnitude longer, will need to account for these effects. We investigate the
impact of neglecting the frequency-dependent detector response for compact
binary coalescences and show that it can introduce large systematic biases in
localization, larger than the statistical uncertainty for 1.4-1.4$M_\odot$
neutron star coalescences at $z\lesssim1.7$. Analysis of $3^\mathrm{rd}$
generation detectors therefore must account for these effects.
