I plan on building the adire kit81's and have some 3/4 oak veneered plywood. It was $67 a sheet and looks like it has no voids. Could I use this or is it a bad idea?
While it worked well for my small sub with heavy cross-bracing and very small spans, I think you're much better off with MDF for a full-range application. In my experience with it, I think that oak ply would resonate fairly high, which is ok, even desireable, for a sub, but might seriously color the output of the Adire kit.
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Go for it. Good bracing will solve most if not all your resonation problems. You may also want to spray the inside of the box with dynashield or a similar mass loading spray. I have also had fairly good luck with a few layers of rubberized undercoating which can be had cheap at any auto parts store.