The most common cause of a whinning sound is the tensioner pulley or water pump. I don't know what a winding sound is if that is what you really meant. If the dealer installed an alternator and new belts they should have identified any of these problems. The A/C applies an extra load to the belt and would add strain to any malfunctioning parts.
The balancer/vibration damper could also be the cause if it is beginning to fail.
I recommend removing the belt(s) after drawing yourself a diagram of how it (they) are routed. Then check each component and pulley seperately to check for binding or rough operation. They should all spin freely and smoothly with the exception of the large one at the bottom (that's the balancer and is bolted to the crank shaft). Pay special attention to any idler or tensioner pulleys. "Bouncing" as you describe is often caused by inadequate tension being applied to the belt. It's also something that would protest the added strain of turning the A/C compressor pulley.
It is possible the dealer technician didn't notice the tensioner was weak. Cost for these repairs depends on exactly what turns out to be the problem. Good luck and I hope this helps.
Thursday, April 14th, 2011 AT 2:11 AM