That noise usually happens when the compressor clutch air gap is too small. When the a/c is disengaged, the speed difference between the pulley and the clutch plate is crankshaft speed (multiplied by the crank:compressor pulley ratio). When it's engaged, the speed difference is zero - same time as your noise disappears.

Look carefully (with engine stopped) for something odd in the area near the gap of the pulley (the only moving part while tha a/c is off) and the clutch (the stationary disc in front of the pulley).

Also check to be sure nothing is hitting the belt due to worn insulator bushings, where the compressor shifts when engaged causing the belt the belt (and noise) to clear.