sound is dampened when it bounces off many different walls and is redirected many time. therefore, i have come up with an idea!
take a section of pipe of equal width to your barrel and about 1/3 the length. drill 24, 3/8 inch holes in it, in any pattern you choose, trying to spread them out as best you can. buy 30 feet of 3/8 inch copper tubing and cut it into 30 1 foot sections, then discard 6 of them. slip each one through a hole and use a piece of tape to secure it.
now, obtain a larger section of pipe, 2 times the diameter of the smaller section and the same length, and 2 reducers to affix them to each other. slide the larger pipe over the smaller pipe, and move all the copper tubing so it dangles in the space between the two pipes. attach a reducer so one end is blocked off.
fill the entire chamber with liquid foam (the heavy duty kind in a can) and let dry.
using a tool of somesort, pull all the copper tubing out from inside the smaller pipe (a long handled pair of pliers should work, leave room at the bottom of the tubing so you can grab it)
affix the last reducer, and put the appropriate fittings to attach the unit to your barrel. in theory the sound should escape into the tubes in the foam and reverberate inside the holes and be absorbe by the foam itself. there should be very little powerloss.
maybe someday ill try this, it sounds a tad bit complicated, but ive been working on the idea for a long time