Talking with Gabe at Rampage, he turned me towards a Helmholz resonator as a means of attenuating (cancelling out or silencing) unwanted frequencies without causing any sort of actual restriction in the exhaust. So I started researching the idea.

https://newt.phys.unsw.edu.au/jw/Helmholtz.html

https://lautsprechershop.de/tools/t_helmholtz_en.htm

At this point I realized I wasn’t as good at math as I thought I was, but during the course of the research I’d found something called a Quarter Wave Tube (QWT). It functions essentially the same way, amplifying or cancelling out a pressure wave within a certain range of frequencies, and the math was much easier.

The meat and potatoes is that you calculate the speed of sound at a given temp, calculate the frequency of the resonance that’s bothering you, in my case it was 91.25 HZ (you can calculate this by exhaust pulses per second based on RPM or just use an audio scanning app on your phone to figure out the problem frequency), and with that extrapolate the length of the soundwave, or distance between pressure pulses. It’s called a quarter wave tube because you want the length of the tube to be one quarter of the wavelength that you want to cancel out. So the sound wave enters the tube, travels to the end, bounces back, and should re-enter the exhaust stream halfway between pulses, thereby cancelling the resonance.

https://www.acoustics.asn.au/conference_proceedings/AAS2012/papers/p79.pdf

Something interesting that they noted in the study above is that the temp inside the quarter wave tube didn’t go too far above ambient, so if we use say 100f as a constant, and 91.25 Hz as the frequency to disrupt, we can calculate the wavelength, and use one quarter of that length as the length of the QWT.

https://www.omnicalculator.com/physics/speed-of-sound

Where lambda is the wavelength…

λ = v/f = speed of sound / frequency

λ = (1159 fps)/(91.25Hz)

λ = 12.7 feet

And to get the length of the quarter wave tube, divide that length by 4, and you get 3.17 feet, or 38.1 inches.

Some notes, if you can integrate a bellmouth orifice where the QWT connects to the exhaust, it will be much more effective, and the closer you can get to the engine, the more powerful the pulses will be and theoretically give you a more powerful cancellation pulse.