Just bought 06 LR3. Took it on the beach twice. Got dug in once. I dug it out but needed to push, wife drove and really gunned the engine while in low range.
No problems but a few days later I opened the rear windows and the thumping noise was deafening. No vibration or shimmy and can only hear it with windows open.
Is this the the cupping problem I've heard about or did I do damage in sand.

 

Nope, the tires ARE noisy but what you're hearing is "normal". I believe it's a combination of cabin air pressure and the way air hits that area of the vehicle (rear side windows) at certain speeds. Try opening another window to offset it OR just close the rear window at speed. Glad to hear that you're already playing off-road. Did you try switching the DSC off when you got stuck in the sand?