What is this high pitched sound my car is making?

Definitely sounds like a loose or slipping belt, often caused by a new belt that has stretched out or a cold belt that is reluctant to move. This typically happens during the winter or during the cold of the morning. It usually goes away after your car has been running for a while and the belt has some time to warm up and becomes more pliable. You should have your mechanic tighten the belt or perhaps change it if the tread on the belt is worn. This is a typical issue with most automobiles, although I have had the same problem on my 2005 Scion xA.