I think you got the same problem with me... Turn the A/C off... does the
whirring sound disappear?

If not, when is the last time you changed the serpentine belt? What is the
current mileage? You probably need to change the belt tensioner.

I recently bought an 86' 190e and found the tensioner in these cars
consists of a rubber grommited arm (bad description sorry).

Basically it relys on a rubber "donut" with metal on the inside and
outside to provide the belt tension.  The connection between the rubber
donut and the outer metal had broken down on mine which allowed the
middle to turn, thereby not providing enough tension.

If you know how to adjust this tensioner, simple relaxing it and
retightening it will let you see whether it still working.  Also the
amount of threaded rod that sticks up from the adjuster when the belt
is tense should be a dead giveaway (the rod shouldn't be sticking out
above the adjustin nut).

My car also had slightly loose alternater bearing (110K miles) and a
very slight wobble to the waterpump.  A new waterpump and a re bushing
of the alternator (65$US) by a local auto electric shop made it purr.

Good Luck,
Marty

PS be careful not to overtighten the serpentine belt tensioner
adjustment as the adjuster will break quite easily (I broke two before
figuring out my tensioner was spun heh)