More specific to your question the "Resonator" is really misnamed. IMO it should be labeled something more like "De-Resonator" because that is its purpose.
A background in resonance. Resonance is basically the effect of multiplying vibration. Typically it will occur at specific frequencies for any given piece of machinery. A good example of this is a musical chord. Press the the right 3 keys on a piano simultaneously. You can hear all 3 tones distinctly, but you also hear a 4th different tone. Another example would be shaft bearing vibration. If you rotate the shaft at xxx RPM the vibration is low, rotate it at yyy RPM and you will destroy the bearing.
In the case of the cummins exhaust, it relates to sound. Sound is a vibration.
To illustration what I mean, I am sure at one time or another everyone has tried to play a trombone (trumpet etc). The vibration source is your lips in the mouth piece. Any one can try to play, but unless you get the vibration of your lips right in conjunction with the right amount of air flowing through the horn all that comes out is a squawk. When you get it right, the sound booms out the other end. That is resonance, or very close to it. In the case of a trombone, move the slide in or out and change the buzzing frequency of your lips and do it well enough you get a chair at the Boston Pops Orchestra otherwise just pack your lunch and go to work as ussual.
Now for further musical relation. Many times, especially non OEM, a diesel exhaust pipe is almost nothing more than a big trombone. The point that resonance is achieved really is base upon the configuration of the equipment. It is engine RPM which causes exhaust gas pulses at a certain frequency, exhaust gas flow speed, size of the exhaust pipe and length of the exhaust pipe etc etc etc..... If the right conditions occur so does resonance and the sound booms.
So the purpose of the "resonator" is to prevent resonance from happening. Specically, the resonator does this by momentarily storing exhaust pressure in the exhaust pipe. This occurs when a pressure pulse moves down the pipe. During the lull period before the next pressure pulse this pressure gets released rapidly. Effectively, it creates a "counter" pressure pulse that messes with pulse frequency of the pipe and hopefully prevents resonance.
Jim