"Whining Noise comes from Secondary Air Injection (AIR) Pump Motor -V101" - a quote from the technical bulletin 05-01 for 2000-2005 Audis.
I guess the motor bearing must be gone - when it engages on cold start it sounds like fire alarm for some 30 seconds.
The cost is ~$360 at http://www.usedpartslive.com
. Anybody has a cheaper solution then replacing the pump, or good source for it?