Nissan Repair: Fan clutch???, fan clutches, fan clutch

Question
My 92 nissan with 191,000 miles has begun to sound like a airplane taking off.  The cooling fan spins all the time and is making a noise when you speed up or add throttle like a propellor of a airplane taking off.  Is my fan clutch shot?  
Can I tie a string to the fan when the engine is cold to see if the clutch will engage. and not break the string until the engine heats up.  If so what should I expect to pay a shop for the replacement?

Answer
A new clutch for the fan will run about $100 from Nissan and it is really easy to do yourself.  Or for about $80 bucks a shop will install one.  I say $100 for the clutch as I would go to Nissan.  Aftermarket fan clutches are not worth the trouble when it comes to fit and balance.  So go with Nissan for the part.