You would hear a very loud slapping noise as the belt came around and smacked the inner wheel well. You would also hear a constant loud rubbing noise transfered from the road surface. It would seem to fill the whole car with the noise and be very unbearable. This would be a very dangerous situation.
Most of the time the tire will start to make a humming sound, often confused with louder than normal road noise. As the tire tread begins to scallop more with high and low spots, the noise will become more obvious and more of a thumping noise.
The usual noise is a ticking or faint thumping sound with each revolution of the wheels, especially noticeable when you pass tall lane dividers and the sound rebounds.
If your had a broken belt or a threw out a chunk of tread it wouldn't necessarily make any noise. The vibration would be a more noticeable indication of dire damage. Unless your running an older tube tire you would more than likely have a flat.