2017 MK3.5 ST1
Thanks for all this info!These are all good ideas for you to consider. Consider building it according to your original layout, above, and then run it to see if you need a resonator in the first place. If you do, then consider locating it ahead of the muffler. Vortex shedding generated by gas flow past the sharp edges of the branch pipe can produce high-pitched noise, but this turbulence can also induce self-excited resonance in the tube, reducing its overall efficiency. A muffler can attenuate some of this noise if it occurs (providing a radius or chamfer at the resonator tube entry can also help). Sound-dampening material in the car will certainly help.
As already mentioned, exhaust gas temperature is a critical factor, and it must be measured under a load and within the rpm range where droning occurs. Adding a threaded bung to the exhaust pipe to accept an adapter for a temperature sensor will make it fairly easy to do this. Measurement can be taken from inside the tailpipe, but this will be less accurate. Another critical factor will be frequency. The best way to figure this is with a noise meter, and apps are available for Android and iOS that can perform a frequency analysis. A less accurate alternative is to calculate firing frequency, based on the rpm range where droning occurs.
If you record a frequency spectrum of the exhaust under drone conditions and the dominant peak in the spectrum is centered at 80 Hz (and this corresponds to the dominant peak in a spectrum recorded in the cabin under the same conditions), then this is the target frequency you want to tune for.
Making the resonator adjustable is a very good idea, but it should be possible to get the length pretty close by careful attention to detail, even when using simplified acoustic theory instead of 1-dimensional analysis or finite element method.
I've been working on a writeup on drone and resonators for the forum and plan to post it some day, whenever I have time to finish it. I'll include the summary to that piece here, in case it might be of some use. I've appended a paragraph from the main text on the effect of a tailpipe and its length between a silencer and the atmosphere.
I’m pretty sure I’ll start with the original build and reassess once it’s on there.