Do fan clutches make noise at different speeds?
No. If you think you are hearing noise from a fan clutch have it checked. My guess the noise you are hearing is comming from the water pump. Either way this needs checked out. Sugestion; take the serpitine belt off ( fan belt ). See if the fan clutch has a bit too much movement. If so it could be going bad & need replaced. Most times a water pump will leak before it makes noise, due to the seal being tore up by the shaft. Check them both.