Can’t think of a formula. There are a lot of variables, but I have some really old actual test notes that might give some tuning frequency data. You might have to “try and tune.”
Also, these are the primary resonant frequencies, so adding damping material behind the panel (don’t let it touch the diaphragm) will widen the response a lot, which is likely a good idea. Triangle corner traps can cover a wider band, being effectively a range of depths.
Like I said, rough estimates. Sorry these are in inches.
1/4″ material (Plywood)
26″ deep (behind the panel) = 40HZ
18″ 50Hz
12″ 60Hz
6″ 80Hz
3″ 125Hz
1/8″ material (plywood)
50″ 40HZ
33″ 50Hz
23″ 60Hz
15″ 80Hz
5.5″ 125Hz
1/16″ plywood
45″ 60Hz
24″ 80Hz
10″ 125Hz
1/2″ no data, but you can probably interpolate a good guess.
Wild guesses:
16″ 40Hz
6″ 60Hz
3″ 80Hz
1″ 100Hz