I find that when the fuel in my tank starts to get low, the tank seems to amplify engine-noises. I get a very tinny noise which sounds like clattering valves, but the sound diminishes quite a lot if I grip the tank with my knees. By gripping and releasing I can almost switch the sound on and off! The tank isn't loose, and there's no problem noise when the tank is full, just that lovely thump-thump-thump. I think the near-empty tank is just acting like a big, tin drum.
If I got some of that sound-deadening material that they use in the engine-compartments of cars - looks like half-inch thick felt - and if I glued a layer of this to the underside of the tank, would it make any difference? What do you think?.
Tom