I had the same happen to my brothers mustang. Turned out to be the rear end i.e. ring and pinion gear. That was wat was making the loud noises on his i would check yours maybe u low on diff fluid or like his needed to be replaced and shimmed correctly
1996 Mustang GT, 17x9 front and 17x10.5 cobra r replica rims, 255/40/17 front 285/40/17 rear at the moment,
o/r x-pipe flow master 40 series dump downs, cai/ram intake, 75mm c&l throttle body and plenum, pi heads and intake swap, msd wires, stock gears, untuned at the moment, no dyno numbers for now.