Mysterious surging hum

I have a 1993 Toyota L/C diesel engine (non turbo),with manually locking hubs, manual high/low range 4wd shift, manual transmission, electronic on the fly push button 4wd engage switch.

Recently the rear differential (I think since it doesn’t make this noise on a lift) makes a surging hum starting at 35 mph, and increasing in pitch as I speed up. The noise is not consistently there, but inevitably it will come back, especially if I hit a solid bump. As I slow down it will decrease pitch to a low slow growl. Braking sharply/coasting/free wheeling/engine off, doesn’t affect the noise.

Can anybody tell me what the problem might be?

Sounds just like a bad U-Joint, you probably have have one bearing cap that has dried up and rusted.
No saving the u-joint once it gets that far, you need to check it, I don’t know about hitting the bump but do check the joint.

Thanks for the input. I failed to mention in my first message that I replaced the spline shaft (male) and u-joint that fits into the back end of the transmission (female socket), as well as the u-joint at the rear diff.

My best guess is what one old experienced Africa hand (I live in Kenya) told me. He thinks it is the bearings in the diff that are wearing out and allowing the various gears to mesh in a less tight configuration than when new. I cant argue with that, its just that I dont want to tear into a Limited Slip Diff without knowing for sure that is the problem.