My name is ***** ***** i hope i can help you today.
I hope you can apreciate that i cannot see, smell or touch the car but i do strive for customer satisfaction with the service i provide.
From what you have said though, it seems as though the free wheel clutch in the alternator pulley has seized up and so is making a noise and causing the tensioner to vibrate. This is nowadays a very common problem with cars as they are fitted on to most vehicles as a way of taking up the stress on the belt under acceleration.
The best way to check this is to remove the alternator belt from the car and then what you can do is ( with the engine switched off), spin the alternator pulley with your fingers quickly both ways while keeping a hold of the pulley and you should be able to feel the inner part of the shaft coming out of the alternator carry on spinning slightly when the clutch is working. When it is not working and is siezed then the inner part of the shaft will not spin on slightly.
To change the pulley you will need a specialist tool that holds the inner shaft tight while turning the pulley off of it.
Now, if when you are spinning the pulley, the inner part of the shaft spins on slightly then you will need to check the alternator itself by spinning the shaft and seeing if the bearing on the shaft is making a noise, but i will say from experience that this is very rare and is usually the pulley itself causing the fault.
I hope this helps you in this matter, but if you require any further assistance with this problem you can keep posting on this thread even if you have accepted my answer as this does not close out the question. Also, if you require help in the future then please don't hesitate to contact me on this site via my profile and i will be happy to help you again.
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Thank you in advance