This condition is probably normal. The whinning that occurs according to engine speed is probably the sound of cold oil rushing through the oil pump, and is normal. The whinning sound not dependant on engine speed after a cold start is the AIR pump.

I remember a post a while back about the oil pump whinning being normal.

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Ali Al-Chalabi

2001 CLK55
1999 Dodge Ram 2500 Cummins Diesel
2002 Harley-Davidson Fatboy
Merlin Extralight w/ Campy Record