  We present a mechanical analog of a quantum wave-particle duality: a
vibrating string threaded through a freely moving bead or `masslet'. For small
string amplitudes, the particle movement is governed by a set of non-linear
dynamical equations that couple the wave field to the masslet dynamics. Under
specific conditions, the particle achieves a regime of {\it transparency} in
which the field and the particle's dynamics appear decoupled. In that special
case, the particle conserves its momentum and a guiding wave obeying a
Klein-Gordon equation, with real or imaginary mass, emerges. Similar to the
double-solution theory of de Broglie, this guiding wave is locked in phase with
a modulating group-wave co-moving with the particle. Interestingly, both
subsonic and supersonic particles can fall into a quantum regime as with the
slower-than-light bradyons and hypothetical, faster-than-light tachyons of
particle physics.
