If I wanted to make a sound-abating enclosure for an air compressor,
I would line the enclosure with sheet lead, as thick as I could
afford. Appears lead is one of the best noise insulation/isolation
materials available, and even thin (1/16") thick material would
significantly attenuate the noise level.
McMaster-Carr,1-562-692-5911, carries it in all sizes & thicknesses. Jim Skladany