I have been trying to stop a squeak coming from the front of the car for the last few months. I have tightened, used belt conditioner, and then replaced the belts for both sides ( alternator and AC ).
Yesterday I was under it replacing the belt on the alternator side again and noticed a bunch of fine belt pieces on the front of the alternator. The belt had been worn down to the cloth strands in the groves. when I started the car it squeaked again so I shut it off and got back under the car. the car had not been ran so everything was cold except for the pully on the alternator it was HOT. I had the wife start/stop the car several times and watched to see if the alternator was moving as expected ( and no squeaking this time) it was and after the 2nd start the pully on the alternator was cold ???????
Is it possible that sometimes the alternator is not spinning when the car is running/started and other times it spins? I took the belt back off and the alternator spun as I would expect it with no real resistance.

 

Spin everything by hand and find the bad pulley, if I had to guess you have a tensioner that's failing and putting the belt out of alignment which is causing it to fray.

 

thanks @cleric670 i ended up replacing both pulleys and that helped a little bit. The squeaking now only happens when the car first starts up and when the AC is on. So now I will slowly tighten the belt.

I hope this fixes the problem.