  As a shock front interacts with turbulence, it develops corrugation which
induces outgoing wave modes in the downstream plasma. For a fast shock wave,
the incoming wave modes can either be fast magnetosonic waves originating from
downstream, outrunning the shock, or eigenmodes of the upstream plasma drifting
through the shock. Using linear perturbation theory in relativistic MHD, this
paper provides a general analysis of the corrugation of relativistic magnetized
fast shock waves resulting from their interaction with small amplitude
disturbances. Transfer functions characterizing the linear response for each of
the outgoing modes are calculated as a function of the magnetization of the
upstream medium and as a function of the nature of the incoming wave.
Interestingly, if the latter is an eigenmode of the upstream plasma, we find
that there exists a resonance at which the (linear) response of the shock
becomes large or even diverges. This result may have profound consequences on
the phenomenology of astrophysical relativistic magnetized shock waves.
