It sounds like there is a bad bearing in one of the pulleys. Are these alternators brand new? Are you 100% sure that it is coming from the alternator, and not some other pulley right next to it? Often times it is a guide or tension-er pulley that is making all the noise.
You can hand check all of the pulleys when the engine is cold. Just take the belt off and start turning them by hand. The crankshaft pulley will not turn though. The others should all turn smoothly and freely. If you find one that does not, that is your issue.
Guide on taking the belt off and putting it back on:
https://www.2carpros.com/articles/replace-serpentine-belt
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Monday, September 4th, 2017 AT 7:58 PM