Sound in Low Gear

I hear a sound that is hard to describe when the car's speed is from 0 to about 10 miles per hours. It kind of sounds like a thin high pitched whine.
I heard it before, and then I had new tires put on in the front. I can feel the vibrations from the noise. I am afraid it might have something to do with the transmission, but I really have no idea.

It may be a sound that is always present, but gets covered up by wind noise and tire noise at higher speeds. Does it make the same sound with no brakes applied as it does when you are putting on the brakes? Some brake pads have a metal finger of springy metal, whose purpose is to scrap lightly against the brake rotor to let you know the brake pads are worn enough to need replacement.
In order to better hear the noise, and learn if its the same on acceleration and braking, you can drive along the rear wall of a large commercial building - with the windows down. Doing this in both directions may let you learn if the sound is coming from the right side or the left side, or is audible in either direction.
If the car is a standard transmission, check that it has tranny fluid in it. And when driving it close to the wall with the windows down, try putting it out of gear to see if the noise changes. It could also be a noise from the rear brakes, indicating a spring has broken inside the drum and is letting something slide around inside there.
A bad wheel bearing usually makes more noise as you go faster. If it were audible at 10 mph it would be very noticeable at 55 mph.
Good Luck...