  The Cherenkov effect is a well known phenomenon in the electrodynamics of
fast charged particles passing through transparent media. If the particle is
faster than the light in a given medium, the medium emits a forward light cone.
This beautiful phenomenon has an acoustic counterpart where the role of photons
is played by phonons and the role of the speed of light is played by the sound
velocity. In this case the medium emits a forward sound cone. Here, we show
that in a system with spin-orbit interactions in addition to this {\it normal}
Cherenkov sound there appears an {\it anomalous} Cherenkov sound with forward
and {\it backward} sound propagation. Furthermore, we demonstrate that the
transition from the normal to anomalous Cherenkov sound happens in a {\it
singular} way at the Cherenkov cone angle. The detection of this acoustic
singularities therefore represents an alternative experimental tool for the
measurement of the spin-orbit coupling strength.
