First determine when the noise is most noticeable.
Drive Noise: Produced under vehicle.
Coast Noise: Produced while the car coasts with a closed throttle.
Float Noise: Occurs while maintaining constant car speed (just enough to keep speed constant) on a level road.
Road Noise: Brick or rough surfaced concrete roads produce noises that seem to come from the rear axle. Road noise is usually identical in drive or coast and driving on a different type of road will tell you whether the road is the problem.
Tire Noise: Tire noises are often mistaken for rear axle problems. Snow treads or unevenly worn tires produce vibrations seeming to originate elsewhere. Temporarily inflating the tires to 40 psi (276 kPa) will significantly alter noise, but will have no effect on rear axle noises, which normally cease below about 30 mph (48 kmph).
Engine/Transmission Noise: Determine at what speed the noise is most pronounced, then stop the car in a quiet place. With the transmission in Neutral, run the engine through speeds corresponding to road speeds where the noise was noticed. Noises produced with the car standing still are coming from the engine or transmission.
Front Wheel Bearings: While holding the car speed steady, lightly apply the footbrake; this will often decrease bearing noise, as some of the load is taken from the bearing.
Rear Axle Noise: Eliminating other possible source can narrow the cause to the rear axle, which normally produces noise from worn gears or bearings. Gear noises tend to peak in a narrow speed range, while bearing noises will usually vary in pitch with engine speeds.