Alternator workshop warning, cause - failing tensioner???

[TonyConn]

Hello,
The Alternator Workshop warning light came on? It is intermittent, although the battery warning light is staying on. There is a thrumming noise which dims the lights on the dash, I think the belt tensioner is failing, and the belt is slipping causing the voltage to fall. There is movement on the tensioner, which ties in with the noise but I am unsure if this movement is normal. When I put a meter on the battery it is moving between 12 and 14 volts. Don't want to pay for a new alternator if the tensioner is the cause. Is there a way to check? Thank you.

[Crasher]

On which car?

[TonyConn]

Hi, It's a 2003, vw passat, 1.9tdi, 145k miles.