Where drone is the sympathetic resonant frequencies in the cabin, also called cabin resonance / harmonics / room gains / room modes / corner loading.

Quarter Wave Resonator is also called side branch resonator / back pressure tubes / resonant frequency / “J” shaped pipe / advanced resonance tuning (Motordyne Engineering) / narrow band acoustic attenuator / standing wave dynamics (physics): which is a “T” off the exhaust pipe with the same diameter pipe, a cap end, no acoustic material, any bends are optional (with 90 degrees being a “J” pipe) and pipe length where longer lengths are required for lower Hz.

Examples: http://www.regimage.org/no-drone-resonator/

The following formula is from several sites including: http://www.enoisecontrol.com/related_ar ... r_wall.pdf

**Resonator length = 0.25 * Speed at Temp / Drone frequency (Hz)**

The 0.25 is for a quarter of the wave length of sound causing the drone. The purpose being to reflect a sound wave back at the exhaust pipe between cycles (at least three quarters of the wave, but probably augmenting the main pulse a quarter of the time). The side pipe is closed and is not supposed to impede the flow.

The speed of sound increases with higher temperatures, but most people use the wrong exhaust gas temperature for diesels, which burn hotter than petrol engines.

Speed at Temp =331.3+(0.606*Temp) m / s where 331.3 is the speed of sound at zero degrees and the temp inside a diesel tailpipe was measured to be 213.4 degrees C.

https://www.fs.fed.us/eng/pubs/pdf/08511816.pdf· PDF file

Speed at 213.4 C Temp =331.3+(0.606*213.4) = 460.6 m/s

Drone frequency – herein lies my problem. There seems to be two ways of calculating the drone frequency.

Method One:

Drone frequency = (2 x rpm where drone is heard) / 60 (to convert the revs / minute to revs per second to align with Hz which is the measurement of cycles per second)

The “2”

In a four-stroke motor, the cylinders fire every second stroke or once every two rotations. In a four cylinder engine, that would be twice per revolution (2 = 4 / 2)

My cabin drones between 1750 and 2000 rpm.

58.33 = (2 x 1750) / 60

66.67 = (2 x 2000) / 60

Resonator length = 0.25 (¼ wave) * Speed at Temp / Drone frequency (Hz)

= 0.25 * 460.6 / 58.33

= 1.97 m at 1750 rpm

= 0.25 * 460.6 / 66.67

= 1.73 m at 2000 rpm

Method Two:

However, I measured 170 Hz at 1750 rpm on my smartphone app and 176 Hz at 2000 rpm. Some record the drone and then run the file through a spectrum analyser app.

Resonator length = 0.25 (¼ wave) * Speed at Temp / Drone frequency (Hz)

= 0.25 * 460.6 / 170

= 0.68 m at 170 Hz

= 0.25 * 460.6 / 176

= 0.65 m at 176 Hz

**So, what length should I make my quarter wave resonator (1.97m, 1.73m, 0.68m or 0.65m)?**

I don't know how to make a variable length tube to test for optimal suppression of the drone.

The other thing I don't know how to do is to make a bell-shaped "T" joint. I was thinking that cutting a 57mm pipe (my exhaust size) three times at 45 degrees and then wrapping the two cut pieces around a normal "T" joint for marking, cutting and welding might work. The reason I wanted a bell-shaped "T" joint is that it supposedly reduces the sound volume by 25 to 29 dB due to catching more of the sound wave as it passes at 90 degrees.

http://data.mecheng.adelaide.edu.au/avc ... h_geom.pdf Thanks in advance