If you ask a stupid question, you look stupid for ten minutes. If you don't ask a stupid question, you'll be stupid forever
The sound you hear is PROBABLY the electric gyro in the turn co-ordinator.
As you probably know, MOST gyro instruments in MOST light aircraft are vacuum driven (the gyros being spun by suction from the engine driven vacuum pump) - but the gyro in the turn co-ordinator is usually electrically driven so that you have 'something' that still works in the event of a vacuum pump failure.