Your P/S belt may be slipping. If it does that, it gets glazed and slips even more. Is the belt glazed/and/or loose. If so replace the belt and see if it stops. Purge the pump by turning lock to lock several times while engine is running. Also, the fluid may be contaminated. The whine is from pump straining at maximun pressure (turning, usually at full lock). Not good for pump or hoses, seals as they may burst. If that doesn't fix it then your pump may be bad 
