Rrrrooooowwwwaawahh. I know that sound personally, it is usually a sound coming from the rear differential. Your Liberty probably has the off-road package and has a trak-lock in there. BTW the Liberty off-road package added a few skid plates namely under the front diff, transfer case skid, and gas tank skid. This package also included tow hooks (2 in the front and 1 in the rear.
The howling sound is the clutches rubbing on each other. A similar situation to turning with a locker. Usually the sound is more pronounced while backing and turning tightly. A good test to see if it’s the rear. Back up straight then turn and see if the noise happens when turning in reverse. Then try backing in a straight line and without stopping, shift the Liberty into neutral then turn while rolling backward. What this does is take the torque off the differential and the clutches in the trak-lock will release. If there is no sound you have found the source of the noise.
Personally, I have had a few Jeeps over the years and several with howling trak-locks, I usually ignored the noise and never had a problem, the noise does seem to get louder over age. Some suggestions; try changing the gear oil (make sure you use approved oil for the trak-lock) or have it looked at by someone qualified.
Keep wheeling those Libertys.
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