  We describe a unique gravitational wave signature for a class of models with
a vast hierarchy between the symmetry breaking scales. The unusual shape of the
signal is a result of the overlapping contributions to the stochastic
gravitational wave background from cosmic strings produced at a high scale and
a cosmological phase transition at a low scale. We apply this idea to a simple
model with gauged baryon and lepton number, in which the high-scale breaking of
lepton number is motivated by the seesaw mechanism for the neutrinos, whereas
the low scale of baryon number breaking is required by the observed dark matter
relic density. The novel signature can be searched for in upcoming
gravitational wave experiments.
