Saab: Saab 1995, alternator brushes, stop signs

Question
When I start my car it beeps at me and the battery light on the dash is lit. When the car reached higher rpms the beeping stops and the lite goes out. At stop signs the process repeats. After it warms up it stops beeping if restarted. Will a new battery stop the problem or do I need a new alternator? Thanks Bob P.S. Your answers are great!

Answer
Bob:
 In all likelihood, its the alternator; more particularly, the alternator brushes. They can be replaced for less than $50.00 by any honest, reputable mechanic. The problem is, FINDING ONE!
 In my experience, most mechanics simply say:"You need a new alternator" for several hundred dollars.
 Hope this helps