Belt hate dirt/oil, left over/burned rubber, etc, on the pulleys.
Pulley(s) can be worn.
Belt can be too tight or too loose.
Either will wreck the belt. Yes, use a wrench to adjust the alt.
Using a clamp will work but be careful cause clamp make it easy to over tighten, and even break, the belt.
see my cave, serpent belt in general engine. many applies to V belts.
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Dr. Ian Malcolm: Yeah, but your scientists were so preoccupied with whether or not they could, they didn't stop to think if they should.
(Jurassic Park)
The Ogre's Fiero Cave (It's also at the top and bottom of every forum page...)