# Supersonic object in circular motion?

I was wondering, what would happen if a person was to stand at the center of a circumference of radius $R$, where a loudspeaker playing a musical note in the audible range ($C_5=523 Hz$ for example) was rotating at a tangential velocity equal in magnitude to sound speed?

Would he perceive any change in the pitch of the loudspeaker? Or would the sound waves destructively interfere at the center?

What would change if the loudspeaker was shut down so that it would be completely silent (but still have volume)?

• If the motion of the source is perfectly circular, then its radial velocity is always zero, regardless of the angular velocity. This means no Doppler effect, no change in pitch, and no destructive interference because the waves will reach the center always with the same phase. This as long as the motion is slow enough to be nonrelativistic. I'm not sure if taking into account relativistic effects something interesting would happen, maybe someone else can shed light on that aspect?
– glS
Commented Dec 16, 2016 at 10:26