I have a galvanized sheet metal radiant barrier behind the wood stove in my shop. Just a couple of sections on the wall. When the dog is out there with me and barks because he want to go outside, the noise is deafening! Of course, it's a high pitched demanding bark; the sound waves bounce off the metal and it sounds like they're even amplified.

Just a heads up to be really, really sure that you know what you're getting.

Wood doesn’t dampen anything. It’s a hard surface that causes even more echo. Carpet will help absorb sound. But only soft surfaces like sofas, drapes, and rugs will.

An improperly designed insulation detail, and improper air sealing, and mixing a vented and unvented assembly, will create condensation. It can and will “rain” in your house. Vaulted spaces are especially problematic because of the lack of adequate air space for a vented assembly and still maintain the required R value.

To know if yours is improperly designed, you’d have to draw it out and indicate the R value. But right away, you need drywall on that first, to aid in air sealing. Metal won’t air seal at all adequately. That vapor barrier on the batts won't either.

Once that detail is accomplished, air exchanges between the two are down to mostly the penetrations in that envelope. That’s where ICAT fixtures come in.

The issue, as Sophie alluded to, is that walls, ceilings, etc have to either dry to the inside or dry to the outside. If you have a double vapor barrier (metal on both sides) and no proper airflow, you will have a problem.

A clear headed detail of where the vapor barrier is, how spaces are vented, where the insulation is, what type, what R value, etc. is needed.

Just an FYI though: Standard metal roof construction isn't vapor tight. There is roof decking, then felt paper (permeable) an air gap with the furring strips, and then the roof.