Hello Im a BMW newbie and got in on the ground floor with a 323i with 140k. It seems like a very nice car mechanically so far. Fluids are good. Seems tight.The only issue I have is with a humming coming from the rear. It sounds more drivers side but Im not totally sure. The noise gets louder the faster you go and is fairly loud at 40mph+. I thought it was the tires at first as they were worn and actually found out that one had a broken steel belt. I got new tires today and the noise is still there. I was wondering what may be the causes? Wheel bearing? Rear diff? Any help and possible costs would be great. Thanks!

most likely a wheel bearing. while moving around 35 mph. try weaving back and forth. you should hear the noise get louder in one direction and quiter the other. the loaded side will produce noise (ie if its louder while you are turning left, it should the the right rear wheel bearing) good luck.