Can You Put Acoustic Panels on a Door?
Updated
You can put acoustic panels on a door, and they'll soak up echo on your side of it, but they barely cut the noise coming through. A 2 in. Owens Corning 703 (opens in a new tab) fiberglass board absorbs nearly all the mid-range sound that hits it (NRC 1.00). Still, at 3.0 lb/cu ft a 2 x 4 ft panel weighs only about 4 lb, and blocking sound takes mass.
The bigger problem is the gap under the door. In PABCO's example (opens in a new tab), one unsealed gap 1/8 in. wide and 1 ft long dropped a wall from STC 46 to 36, and the gap under a typical door is a lot bigger than that.
Want a quieter door? Start with a sweep or threshold seal and perimeter gaskets, then go to a heavier slab. Soundproof door panels walks through those options, and the soundproof panels guide explains the difference between soaking up echo and blocking noise.
If all you're after is less echo, GIK (opens in a new tab) says a panel can go on a door (a solid-core one especially), as long as the door still opens and closes all the way and the fasteners suit what the door's made of. Clip and screw details are in how to install acoustic wall panels, and you'll find more answers in the soundproof panels FAQ.