You might want to get more information. The whine could be the alternator or something else. A bad diode in the rectifier bridge could result in a whine. The DC voltage is one measurement, then you can measure the AC content of the alternator. - - Maybe this is too much, is there an OReillys, AutoZone etc near that could test the unit? Their equipment will measure regulated voltage, and AC content for the health of the rectifier bridge. That can verify the issue or eliminate the alternator( or one of its many parts) as the root cause.
Also, how many hours on the unit? An alternator is not that complicated internally, rotor, brush holder, regulator/OV, and the diode bridge. If you have a number of hours it might be a good time to replace the bearings (at least on the pulley end) brushes etc. The stator and rotor should last a very long time.