The coherent decay of a nuclear exciton created by synchrotron radiation in
spatially separated targets is studied in the presence of ultrasound (US)
vibrations in one of the targets. The time evolution of the nuclear exciton
perturbed in such a way is described by interference between the wave pack
ets re-emitted by both targets and radiative coupling between the targets.
Since the condition for initial phasing of the wave packets and coupling ca
n be restored periodically by US, strong intensity enlargements in the time
response, called nuclear exciton echoes, are observed. If the targets have
different resonant energies quantum beats arise which are frequency modula
ted by the US perturbation. A complete dynamical theory is presented which
provides a quantitative description of all experimental results discussed.