  Resonances usually result from wave superpositions in cavities where they are
due to the wave spatio-temporal folding imposed by the boundaries. These energy
accumulations are the signature of the cavity eigenmodes. Here we study a
situation in which wave superposition results from the motion of a source
emitting sustained overlapping waves. It is found that resonances can be
produced in an unbounded space, the boundary conditions being now defined by
the trajectory. When periodic trajectories are investigated, it is found that
for a discrete subset of orbits, resonant wave modes are excited. Trajectory
eigenmodes thus emerge. These modes have three attributes. Their associated
resonant wave fields are the Fourier transform of the source's trajectory. They
are non-radiative and they satisfy the perimeter Bohr-Sommerfeld quantization
rule.
