1hotz is almost dead on, but forgot to mention that if the box is under 1 cubic foot (roughly), or has short dimensions, then it won't flex and 1/2" would be fine. But, I'd go one step further and use 1/2" Baltic Birch plywood. It is stiffer and more rigid than MDF of 3/4" thickness, and best of all, it is lighter than the 1/2" MDF. SOOOOOO, you can make your box more rigidly damped AND lighter weight. It does cost about double what the MDF does, though. I also find the birch ply easier to work with as it is real wood and not dust/glue, and it can be finished in more versatile ways.