jeff thats pretty funny. I like that.
Jim, you are exactly right about the whine. There is slop in it.
My brothers differential does that because the old one broke and someone didnt align the gears when they swaped it, so it rings as the pinion comes off the spur gear like jim explained. We changed the fluid and it helped a little.
See every differential is a little different, they have to be shimmed side to side, so if you do get a another one, make sure that someone aligns it properly. My dad was explaining how to do it, but I forgot. I can ask again.
Id just change the fluid more. It can probably whine for a long time because the differential is one of the most reliable parts on cars anyway.