So last year some time, I had Rampage Fabrication build me a 3.5 inch turboback exhaust. One large 3.5/3.5 vibrant muffler, split at the rear suspension to two 3 inch tips. Looks stock, idles quiet, sounds pretty good. Well, good until you get between 2500 and 3000 rpms, then a horrible, booming, brassy, 350 Z-ish noise comes out. I basically just drove around the noisy spot for months, stayed below 2k rpms, got fantastic gas mileage, and if I had to stand on it, it’d jump above 3k anyway. My wife didn’t like driving the car at all anymore, people would look at her in traffic, even at part throttle it was nasty, and with the APR flash, at moderate throttle it stays right in that range all the time.
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.
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.
