  The Doppler effect, the shift in the frequency of sound due to motion, is
present in both classical gases and quantum superfluids. Here, we perform an
in-situ, minimally destructive measurement, of the persistent current in a
ring-shaped, superfluid Bose-Einstein condensate using the Doppler effect.
Phonon modes generated in this condensate have their frequencies Doppler
shifted by a persistent current. This frequency shift will cause a
standing-wave phonon mode to be "dragged" along with the persistent current. By
measuring this precession, one can extract the background flow velocity. This
technique will find utility in experiments where the winding number is
important, such as in emerging `atomtronic' devices.
