If you are thinking belt related, maybe the tightened belt put some extra side load on the alternator or something? Get some tubing to act as a stethoscope and see if you can hear it, probably engine speed dependent after it warms up? If not, then coincidence on the belt and check all the other stuff.
Is it a constant noise, or pulsing? Any idea if it changes with vehicle speed, engine speed, or driveshaft speed? See if you can find a construction zone with concrete barriers, that can help you determine where the noise is originating.
Side story, I had my wife's old truck start making a soft grinding, seemed to come from the back, not the front. Both hubs had the same heat signature, and didn't sound like it was driver side or passenger, maybe the middle? But didn't sound like a bad differential either. I was in the process of jacking it up to see about running it in gear on stands (not great, I know, but was making efforts to do it as safely as possible) when I found the culprit. A cardboard box she had stuffed between the cab and bed MONTHS before slipped down and was riding on the driveshaft. So keep an eye out for anything out of place, sometimes cars do weird stuff...