I'm wanting to build a small outdoor attachment off my shop to house my compressor in. I'm going to pour a cement slab and then build off of that. I'm doing this so save space but mostly to hide the noise of it while I'm working.

I'm thinking of using 3/4 plywood for the body and then installing 1/2 foam board to the inside of the structure. Is there any better way to sound proof the box?