I had to replace a belt tensioner in my '97 at about 50,000 miles. The bearings were shot. I confess that I have taken the car wash wand to my engine compartment, which might not have helped any. It didn't cost very much.
I had the same problem with my 1999 C5 coupe. The dealer replaced the tensioner and the alternator with revised parts, per a TSB. The alternator (called a generator by GM) has a clutch pulley that was used for A4 equipped C5's beginning with the 2000 model year. The replacement parts eliminated the shift rumble noise. If you pay for the replacement generator with the clutch, it is expensive. Good luck.
The new generator w/decoupler pulley (clutch) was a line chasnge made at the factory effective with the 2001 model year for automatic transmission cars only. The 2000 model year cars all had the original generator set up without the decoupler pulley.
There are two tricks that take a little common sense when working with a running engine. You might do damage to both body and car, if not careful!
One trick to find out if the belt is making the noise and not another part, (i.e. tensioner, alt. bearings, A/C pump... etc.) is to take a bar of soap and touch the outside of the belt area. Be safe enough, so as not to get a hand or part of clothes (long sleeve) caught around any pulleys. If the noise goes away, it's the belt.
The same scenario stated above, but this time, use Gasgacinch.
If you have something like 3M Tack spray, this would also work. Just be careful about the vapors and fire!!
If the noise is still there, then rule out the belt. Next thing is to remove the belt and spin the pulleys. One should make an obvious noise that you are hearing. Don't assume (it's the tensioner)!