Exhaust Drone + 1/4 wave resonator = quiet

[fourtrax]

Ok, So i sold the Tacoma and got me a Tundra. one of the first things to go was the smaller then factory muffler and tail pipe the PO had installed to pass inspection just before he sold it to me. I was wanting to do a cat back in stainless exhaust and after some research i settled on a MBRP dual 2.5" into a muffler and 3" out the rear corner, as I have always preferred a good single exhaust over dual pipes. cut the old pipes off installed the new one in about 45 minutes. started up, sounds great, a tad louder then then neighbors might have wanted but, oh well. only bad think is that i have this deafening drone in the cab from 1800 -2000 rpms, which happen to be both the rpm for normal acceleration and for cruising 68-75 mph. so i had to find a solution. after some surfing I happened across a thread on Helmholtz branch (1/4 wave) resonator ( also called a J-pipe) sounded a little out there but it had some science (math) to and i was intrigued.

For v8 engines drone usually starts right at 2000 RPMs.

for a general rule of thumb
V8s fire 4 times per revolution.
6 cylinders fire 3 times per revolution.
4 cylinders fire 2 times per revolution.
RPM is in minutes, so again divide by 60 to reduce to seconds.

We also need to know the speed of sound. It varies with temperature, but is generally accepted to be 1160ft/sec @ 100F
( i went with 100F because the branch pipe was capped off at the end and there is really no Gas Flow it is only used for the sound wave).

Speed of sound
90F = 1150 fps
100F = 1160 fps
110F = 1170 fps
120F = 1180 fps

Math to determine frequency (f) of the drone:

f = RPM * pulses/rev * (1/60)
f = 2000 rev/min * 4 pulses/rev * (1/60)
f = 133.34 pulses/second = 133.34Hz

Math aside i still had variables i wasn't sure how to quantify, what would the temperature actually be of the air in the branch pipe, was the frequency coming from the exhaust pulses, a vibration, or body panel?

I download an app called SPECTRIOD to my smart phone and ran it while driving I found I had two sound waves that were in the drone. the starting frequency was 120hz at about 1800 rpms and at about 1950 rpms there was a second frequency of 129HZ. I also learned that the 1/4 wave resonator worked in a pretty narrow band. The theory is to reintroduce a sound wave into the exhaust that is 180° out of phase with the drone frequency. This is what the 1/4 wave resonator tube accomplishes. The resonator tube needs to be exactly one-fourth the length of the full resonant wave. The sound wave enters the resonator tube, bounces off the capped end and re-enters the exhaust stream. At this point the amplitude is exactly opposite of the drone frequency and will cancel out the drone.

for the first frequency 129HZ
1160ft per sec / 129 Hz = 8.992 ft
8.992 ft / 4 = 2.24 ft
convert to inches 2.24 ft * 12 = 26.97 inches

for the second frequency 120HZ
1160ft per sec / 120 Hz = 9.667 ft
9.667 ft / 4 = 2.41 ft
convert to inches 2.41 ft * 12 = 29 inches

I decided to split the difference and opted to go with a 28" length of pipe for my resonator.
I want to the local exhaust shop in Apex, cause they had stainless. we cut a 2.5" hole in the 3" tailpipe after the muffler at the top of the hump over the axle. we then welded a 28" piece of 2.5" pipe 90 degrees off the tailpipe running it toward the other side of the truck parallel to the axle between the axle and the spare tire. we capped it and secured the end with a hanger.

3 things that are key to making this work once you find the length.
1. the resonator must be 90 degrees off the flow (after you enter the resonator tube you can go straight, curves, spirals, what ever)
2. any bends need to be mandrel, if you kink crush or distort the pipe you will distort the sound wave.
3. the end of the pipe need a cap that is flat and at 90 degrees to the pipe.

I was blown away on how well this actually works, i have ZERO drone and the exhaust level in the cab is actually about 7db less. it still has a growl and all the volume if i step on it but, cruising around and on the highway it is just background.

Something to think about if you have a exhaust drone in the cab.

** to be fair i have summarized and combined information i have found on multiple post throughout the web on 1/4 wave resonators. none of the sites i visited had what i thought was the complete detail to make this happen.

 

[Fabrik8]

This is the exhaust equivalent of the helmholtz resonators that most cars have had on the intake for the past 10-15 years for torque curve widening. Good stuff.

 

[Ron]

There is so much wrong in this post... l try to respond in long form tomorrow, but it will be later afternoon.

First your "fire per revolution" is wrong. 4 stroke, per cylinder * 8....math don't work.
Speed of sound varies with frequency.
DB is a logarithmic scale.

Start with those three, add an intake tornado spacer and a fuel resonance filter and viola.

 

[a_kelley]

First your "fire per revolution" is wrong. 4 stroke, per cylinder * 8....math don't work.
...
DB is a logarithmic scale.

Yes they fire half the cylinders per revolution. Cam runs at half crank speed. Two of four strokes per revolution. Therefore half the cylinders fire per revolution.

dB is a log scale yes. But what does that have to do with if his app reports dB?
And as far as speed of sound, he didn't say it was xxx in all cases, just Generally Accepted.

 

[shawn]

This is the exhaust equivalent of the helmholtz resonators that most cars have had on the intake for the past 10-15 years for torque curve widening. Good stuff.

Oh, you mean that "stupid" "restriction" that the factory engineers put on there that definitely needs to be taken off and replaced with a chrome pipe....?

 

[paradisePWoffrd]

resonators like you installed are a good solution to keep in mind for buggies and other offroad rigs. They can be much easier to package vs large mufflers and such, and keep the noise in the "cab" down.

While not as cool, "resonators" are being used in a number of higher end cars these days to quite the interior. Basically they record the resonance frequencies within the cab and then place "speakers" under the dash to resonate at the inverse frequency to cancel the sound noise.

 

[a_kelley]

Also known as active noise cancelling.

 

[BrianGreen]

Google BAMufflers. He makes exhaust for Tundras and a couple other trucks using that principle.