J-pipes do more than dampen the sound. They elliminate it. Basically, since the J-pipes are sealed, consider them a "high pressure" area.

Let me back up a little bit here. Exhaust gasses are racing (excitedly) out to the end of your exhaust tips so they can reach the air, where the pressure is lower than where they came from (The combustion chamber and various exhaust components, actually!) ... so Exhaust gasses want to "get out" to an area of low pressure. Got it?

So since the J-pipes are sealed, no real "exhaust gasses" ever get into the J-pipes to begin with. To the exhaust gasses, the J-pipes are simply another wall that is not an option to exit from.

Sound waves are completely different. Sound waves can travel through just about anything... water, metal, etc. Sound waves are a byproduct of combustion engines. If you've ever heard "open headers" like on race cars or demo derby cars, you know what everything "really sounds like" right out of the combustion process. Normal factory stock exhaust systems are usually over-engineered to appease the 'transportation' type of person who does not like hearing engine noises. This is why enthusiasts upgrade to aftermarket exhaust components.

Drone is usually solved by a nearly silent stock exhaust system (over-engineered) ... and drone is the uncomfortable level of soundwaves, as they reverberate not only in the cabin but also in your eardrums.

What J-pipes do is allow the soundwaves to enter into the "mouth" of the J-pipes, and if you remember cosine/sine graphs from math class, you know what sound waves generally look like. Now the sound waves are inside this capped "tube" ... bouncing off each side in a certain pattern (Hertz rating) ... then BAM. they hit that cap at the end of the J-pipe. Now those sound waves are reflected in the exact opposite direction, in exactly the inverse wavelength pattern (effectively cancelling out that calculated soundwave pattern) and then at the "mouth" of the J-pipe, they safely exit back into the exhaust stream and out the rear of the car, now the inverse of what they were when they entered the J-pipe. The magic happens when the two inverses collide, within the J-pipe itself. This actually elliminates the sound that was calculated (or in other words, the exact overall length that you made the J-pipe).

If your calculation is wrong, you will not elliminate the sound.

This is completely different than "dampering" the metal to make the vibrations a different frequency, like you seemed to have suggested. While that works in some applications, the source of this drone is the engine itself, with it's specific engine harmonics. As soon as that stock exhaust system is replaced with a "performance" exhaust system, you get the nice rumble of a freer flowing exhaust system, however, now those engine harmonic traits (drone in certain RPM and engine load combination conditions) show their ugly head. J-pipes to the rescue!

Simply put, the formula for determining the length of a Helmholtz chamber used to knock out a drone frequency is:

1100 feet/second (roughly the speed of sound) divided by the target frequency you're trying to eliminate (in cycles/second) gives a full wavelength in feet per cycle. Divide this number by 4 to get a quarter wavelength (a much more convenient length to work with). Finally, multiply this wavelength by 12 to get the chamber length in inches.

Tap this length of pipe into the exhaust tube, making sure the other end of the pipe is capped off, and you have a Helmholtz chamber that takes the annoying frequency and bounces it back into the flow 180 degrees out of phase, knocking it out. The results: no more drone.