If your vehicle is showing rumbling noise from the rear that changes pitch when letting off the gas, here are the most likely causes and the parts you'll need to fix each one.
Bearings inside the rear differential support the gears. When they wear out, they produce a rumble or whine that distinctly changes pitch when transitioning from accelerating (load) to coasting (no load).
The U-joints connect the driveshaft to the rear axle. A dry or failing U-joint will cause a rumbling vibration that often changes intensity or pitch when you let off the throttle due to the shift in driveline torque.
If the rear differential leaks fluid, the gears and bearings lose crucial lubrication. This causes a loud rumble under load or coast, often occurring after a missed service interval or an improperly sealed drain plug.
A failing muffler or broken exhaust hanger can cause the exhaust pipe to resonate against the body. The pitch changes immediately when you let off the gas because engine load and exhaust pressure drop.
While wheel bearings usually change pitch when turning, severe wear can cause a constant rumble that shifts slightly in tone when vehicle weight transfers forward as you let off the gas pedal.