In the "old days", it was pretty simple. You had a can full of stuff. If it was a glasspack, it was filled with fiberglass

I have now a "straight through" design in the can. If you look through one end of the can, you can see straight through to the other side ... nothing in the way. It does have a bunch of small holes outside of the pipe running straight through.

The only thing I can think of is that idle or with your foot off cruising, the gasses are flowing slow enough for them to move into the little holes and then back out (I am assuming there is stuffing in the can behind the holes)... BUT, if you put your foot into to, the gasses are flowing much faster and so straight through ... not going into the little holes and hence, louder.

Does this make sense?

 

That's pretty much it, except that the holes aren't for the gases, they're for the sound waves. The gases themselves don't have to travel through the packing for the muffler to be effective.

Picture a champagne cork "popping" out - all of the sound waves are released to the atmosphere at once, hence the loud "pop". If you were to gradually introduce the sound waves to a larger volume of air, you would reduce the intensity of the sound. That's how a muffler works. The sound waves travel back through the exhaust pipe until they reach the muffler, where the holes in the pipe release the pressurized sound waves into a larger volume (the muffler). as the sound waves travel through the packing, some of their energy is converted into heating the packing fibers and causing the packing fibers to move.

Since there are quite a few of these holes in the exhaust pipe, the sound waves are gradually introduced into the larger volume of the muffler over the space of a foot or so. These weakens them considerably, so the intensity of the sound is reduced by the time it reaches the end of the tailpipe.

Note that I don't know whether the MINI mufflers actually have packing material in them - not all OEM mufflers do. They may be working strictly on the "gradual introduction to a larger volume" principle.