Logan, I don't know what the whine is for sure, but my guess would be either the alternator or the power steering pump. I am assuming that the AC compressor is not running. Doesn't sound like the compressor anyway.
Try loading the alternator by turning on headlights and heater fan. See if the sound changes with load. Try turning the wheel slightly left and right. See if sound changes with steering action. This should help to narrow it down.