High pitched whine from either the furnace blower fan or motor
Turn off the electrical power to the furnace and then take the blower door off the furnace. Reach into the blower in the end opposite the motor and try to wiggle, lift or other wise move the blower fan up and down. if it moves up/down you could have worn motor bearings. If it doesn't move then try as @George Anderson wrote. If this is an older unit the bearings could be in need of lubrication. Note, that some motors can not be lubricate which would indicate a need for the motor to be replaced.  Hope this helps.