I assume by tightening the fan belt, you mean the water pump/alternator V belt.
That being the case it could be your alternator bearings. Try removing the V belt and running your engine (NOT FOR TOO LONG THOUGH AS YOU WON'T HAVE A WATER PUMP CIRCULATING THE COOLANT) and see if the noise is still there.
If the noise goes then you may get away with slackening the V belt a little, as Veedubgti8v has suggested.
If it turns out your alternator bearings are knackered, they are replaceable.
If the noise is still there then it is as m4nesh suggests, your timing belt tensioner.