Changed battery, now a soft whining noise

Lately with the cold weather, sometimes the car will start, other times it won't start without a jump. The car is five years old and with the original battery, so I figured it is time to change it. I just put a new battery in, then when I started it, I hear a whining noise. It is a soft quiet whine though, but I notice it. And it was not making that sound before. What could be causing this?