Being supercharged on a 3.8 there is a kind of winy noise when the boost kicks in.Got same sound when idling..Dont sound like an issue sounds like it has a gear drive is the best explination..

Are you aware that the oil in the supercharger needs to be changed every 30,000 miles? https://www.youtube.com/watch?v=JpvwtgYlJFw

http://www.gminsidenews.com/forums/f53/grand-prix-supercharger-oil-9145/

I believe the oil is supposed to be checked every 30,000 miles, not changed. If the oil level is low, indicative of a leak of some sort that will need to be addressed and then possibly new oil put in. Unlike the engine, the supercharger is a closed system so the oil has no opportunity to get dirty like engine oil does. It is also an extremely high grade synthetic oil which does not break down. Most superchargers, including the several I have owned have never had their oil changed. I have run mine to 180,000 with no problem and most shops and dealerships follow the GM recommendation of checking the level and topping up if needed. The Eaton supercharger on your engine is a pretty tough part and it is unlikely there is a problem with it. They do whine a little bit which is what you're hearing and an aftermarket air intake does not muffle the sound like the stock one does so its a bit more noticeable. Keep on driving and enjoy the whine. It's the sound of performance.