Yeah I'll have to do that and see what happens maybe loose and dirty which I hope instead of buying a new one.I have replaced 2 alternators with the same issue. I noticed the whine too and it was worse if I was using accessories like the lights, radio, etc. In my case the battery was either new or checked out as ok like yours. Putting in the new alternator and no more whine. Did not have any further charging system issues.
It is good advice from pontiacgp in checking your wires. Other cars I have looked over had buildup on their battery connections and bad cables which caused charging issues.