2004 Pontiac Grand Prix Noise when accelerating

My wifes 04 GP has been making a noise when accelerating. It almost sounds like a low pitched whine. When at rest the car makes no noise and I dont think it's pwr steering bc I can turn the wheels at rest and the noise is not there, plus I've checked the fluid and it's fine. However I did notice that when I took a look under the hood the alternator keeps spinning a short while after the car is shut off. On my car the alternator stops after it's shut off. Could this be an alternator problem? Or is this a hub bearing thing like everyone elses Grand Prix's? I've taken it to a mechanic and they dont know.
Thanks fo rthe help.