If it is real cold out when i start my car in the morning it makes this whining sound. once it warms up for a minute it goes away. i changed the belt and thought i was good, a week later it started againd. i had a shop check the bearings in the tesoiners when i changed the belt, they said they where good.
heres a vid:
http://s49.photobucket.com/albums/f2...t=DSCN0789.flv

 

Sounds like the alternator whining, had that happen with my car. If you don't have a mechanics stefascope than just take a long screwdriver put it on the alternator housing and put you ear on the pastic end and listen for loud grinding. By the sounds of that clip, its sounds like alternator though.

 

bump

 

Tell your wife of G/F not to stand next to your car when you start it. j/k
Sounds like the power steering pump