Humming noise coming from the rear end

Have you checked the fluid in the differentials? Any signs they have leaked in the past.

Another possibility,

I made some pictures/ diagram several years back, sort of when I was barely computer literate and had not long been a member. My choice of colors as well as the lighting had much to be desired.

Get on level ground (I prefer grass) Chock your wheels (front side and backside of one to prevent rollage in either direction)

Because this is a Liberty, you may not have room to crawl under. So you might have to do this on concrete using jack stands.

Back when, we'd just straddle a ditch or jump it up on to a curb. Regardless, chock and BE SAFE!

Now stick it in neutral so the transmission do not have it 'bound up"

Let's try my pictures now for what to check and how.

If they are too crude, let me know and I explain them.

But in the end, return here with your observations.

If indeed this is the issue you are having, you say yours hums, on my CJ-5 and Willys they will sort of quietly chirp when I let off of the gas and they are pushing (instead of being driven) I can catch the sound right off before they get worse.

Pictures below- your turn

The Medic

Could be play in rear end differential between ring and pinion gears.

Unless you are removing the cover (catching the gear oil) and inspecting the oil and inside the housing, sticking something in the fill hole just is not going to cut it! A chunk of metal will sink to the bottom!

Do the easy stuff first (like checking the universal joints).

I looked at a truck for a lady once. It was said by a shop to need a transmission, maybe even a transfer case. They did not dig real deep, they just drove it and gave their opinion to her.

I drove it and it started making a racket at about thirty five mph. Sounded real bad. I crawled under it so see if anything was leaking or obviously torn up (I am not much on automatic transmissions)

I looked around pretty good. Made my way back towards the rear axle. There above my head was a small black shopping bag (a gallon of milk would not have fit into it) snagged on something. Upon removal and another test drive, I told her I had fixed the transmission and transfer case. LOL!

Not wanting to get you all excited with that story, But it can be "Not so serious".

Check the joints, do it right. I hope you understand my pictures.

Other stuff could be wrong, eliminate the easy and obvious stuff first.

While you are under there.

Your rear axle tends to/tries to 'nose up' while torquing under power while moving forward, letting off the gas it tends to drop (maybe not much, I am speaking of the middle where the drive shaft connects on). Look for things that might contact the driveshaft when it noses up. A plastic shield scuffed up/ something metal with a shiney spot/ even road kill wedged in there.

A common good joke that used to be played on people was to get one of those big heavy nylon zip ties and zip it onto the victims driveshaft. This might quickly be caught onto as it slapped the underside of the car. I have seen it go on days and days while the victim thought his vehicle was about to bite the dust. Usually it did not take long for the zip tie to beat the long tail off and the noise would cease.

I cannot imagine what kind of immature person might do such a stunt to a fellow human being. LOL!

News?

The Medic