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I'm not an acoustics expert, but I have a vocal booth roughly 5x5 with the ceilings and 3/4" plywood walls covered in 4" acoustic cotton with a GIK tritraps in the corners (when I can get away with them spacewise).
It sounds good, dry, but good and not boxey as long as you stay more than a foot from the walls. Put a mic too close to one of the walls or ceiling and you get a boxey sound from reflecting low-mid frequencies, I'm guessing.
So, depending on the materials I'd say 4x3 would leave you a very small sweet spot for mic placement. 5x5ish would be the smallest I'd go. 4x6 would be quite usable, IMO, and you might even get borderline claustrophobics to go in there :-) The bigger the better though.
It may not matter at these small sizes, but I would ask for some advice as to the proper ratios for the sides of the booth. Exactly 5x5, or 4x6 probably would not yield optimal results. But, like I said I'm no acoustics expert.
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