Since I presume you have heard no clunking from the suspension, it seems like a torque related or driveshaft rotation issue. Odd that it only happens in reserse, which makes me think of a loose carrier bearing cage on one side.
Get the car on a lift. Have someone put it into reverse while looking up. You should immediately see whats going on.
I would be careful. If it is violent in reverse, it could be horrible in drive.
I had a friend in college who ignored a loose driveshaft at the transmission on an old Chevy. We kept warning him. It dropped right at a culvert, jammed and then rammed into the differential, tore it out, took the gas tank and a lot of his trunk with it.
He at first thought it was a rear wheel coming off because he saw one roll by his door. It was the loose spare that got launched out of the trunk. I used to have a picture of it. Talk about a violent event!
'03 E320 Wagon-Sold
'95 E320 Wagon-Went to Ex
'93 190E 2.6-Wrecked
'91 300E-Went to Ex
'65 911 Coupe (#302580)