I have noticed that my M3 makes this noise when accelerated heavily and the lsd takes on. It almost sounds like the lsd is "catching and releasing" in a fast pace, almost similar cutting sound than when doing full abs braking.
Initially I thought it was the DSC limiting the spin but tested this with DSC off and I still got the noise! I also tested by dumping the clutch from stand still at about 4000-5000 rpm but that way got normal wheelspin with no banging noise. So the noise only happens when accelerating hard from low speeds and also on low friction (wet) surfaces.
I do not normally mistreat my car or try to deliberately wheel spin it but have gotten this noise a few times recently when accelerating on wet roads. On normal driving conditions I don't get it unless accelerating extremely hard on first or second gear. The car is manual and has 44k miles.
Any idea what might be causing this noise? Is my diff broken or could it be the bushings or quido? I'm taking the car in this week for brake fluid change and software problem so will mention this but any insight on the matter might help locate the problem!