Interestingly, as the SPL of the sweep is decreased, we can see the emergence of some small acoustic reactivity at the resonant frequency. This fits with the notion of non-linear effects, and further suggests that some neck geometries are just "bad" even if they do support resonance.
I just wanted to pick this up. The approach I'll outline below isn't a particularly scientific approach, but it is a handy way of getting an order-of-magnitude idea of what might be going on.
Let's say we have a 12" driver in a sealed box. To produce 100dB@40Hz, 4.8mm of excursion is required:
http://www.baudline.com/erik/bass/xmaxer.html
Now, let's imagine for a moment that we wish to absorb that 100dB@40Hz, using a bunch of tiny drivers distributed across the opposite wall. Qty 1000x 0.25" (approx - there's a note on the website regarding radiating diameters) drivers would each require an Xmax of 11mm to produce an identical SPL. NB - Xmax is a one-way measurement.
Given that the perforated board is often only a few mm thick, the "slug" of air inside the perforations is being pushed very much further than the thickness of the board.
Consider, for a moment, an imaginary ported box where the air is being shoved that far through the port and out the other side, and it becomes intuitively obvious that small-diameter holes will quickly become overloaded. The solutions might include larger-diameter holes, or simply using many more of them.
Further notes:
- The grid of holes could be simulated in something like Hornresp, a loudspeaker simulator, to calculate the Helmholtz resonant frequency. Imagine virtual cabinets stacked in a large grid. Each is a ported box. Volume of air within the imaginary cabinet is your simulated volume, and you have the "port" dimensions already. Hornresp can also simulate chamfers (both sides), peak air velocity, etc etc. You'll need a generic loudspeaker input so that the simulator can have something to "drive" the acoustic chamber, but keeping that generic loudspeaker constant while varying other parameters (depth/area of cabinet, port dimensions) will allow comparisons.
- As hole diameters tend towards the very small and numerous, the surface area to volume ratio of the slug(s) of air will change, in the direction which provides more resistance to the flow of air through the hole. We've seen above that this will make them non-linear in their absorption as incident SPL changes.
- Staying in the world of loudspeaker design for a moment, there's a sliding scale between Helmholtz resonators and quarter-wave resonators. I'd suggest that when the aspect ratio of an absorber passes about 5:1, there's likely to be quarter-wave (and harmonic) resonances happening as well. Putting a "port" on the end turns it into a mass-loaded quarter-wave resonator, where the "slug" of air at the end will act as an additional mass on the end of the spring.
Apologies for the brain-dump. I read the first few pages and was excited to contribute.
Chris