[serialk11r]

So I mean it's actually not that complicated, Helmholtz resonance is just air in a closed area acting like a spring, as air is compressible. The behavior is not exactly like a spring obviously since it's more complicated.

Okay so the examples I can think of would be:
1. Blowing over a bottle makes sound, or any other wind instrument.
2. Opening your car windows at speed creates that buffing noise.
Bernoulli's principle => blowing over the opening creates slight decrease in static pressure, so the air inside the space pushes out, but the air rushing out has "inertia" so the pressure manages to drop below equilibrium and the air moves back into the space, and you get this resonance.
3. If you blow straight into a soda bottle in a quick burst, you may be able to detect sound for a short period afterwards. This is like playing a note on the flute really shortly, the sound doesn't cut cleanly off, but rather continues with diminishing amplitude.
The decay is faster than on say a stringed instrument because steel strings store much more potential energy by comparison.

Where it could possibly come into use in an air intake would be at the intake valves. The front of the car can be assumed to have approximately constant pressure. The side of the intake tract that is changing is at the valves: when the valve closes the pressure wave will hit the intake valve and "bounce back" since it would create an area of high pressure. Now we have a closed cavity with an opening to the atmosphere. While the intake valve stays closed the wave will travel to the opening of the intake and then for the same reason the wave will reflect back. If you open the intake valve just as the area of highest pressure reaches the port, the wave keeps travelling into the cylinder (where the velocity of the wave reduces and hopefully the high pressure zone stays inside the cylinder). I guess this could be called Helmholtz resonance except this "resonance" lasts only 1 period of the wave, so the use of that term is slightly unnatural.

If the engine speed and the period of the wave match then this works well, but you'd need a way to manipulate either the length of the intake or the speed of the wave to make it work. Exhaust tuning should actually work by exactly the same principles, I think Honda stuck "throttle plates" into the exhaust of a bike before to get the velocity of the exhaust gas wave so that it would reflect back and have the area with lowest pressure be at the valve when it opens. One idea I had for engines that cannot use variable intake duration (hello rotary) is to stick an "air motor" (variable geometry turbine) into the intake, as a way to reduce throttling losses. You could combine this with a second intake tract as a bypass, and it would be a more fancy variable frequency intake.

As far as your idea goes, I think that's about right. I think it would work with just one throttle plate, although if you have 2 different length runners you could get a wider range of frequencies. You would be right to say something bad happens where the 2 meet, because if you have one throttle plate closed, the other open, then the tract with the closed throttle plate now exhibits the same effect, and the pressure wave will start to travel up that tract. If the throttle is completely closed this isn't a problem, now the effective runner length is the sum of the open runner and the distance between the place they meet and the closed throttle. But if this throttle is partially open, the wave will "split" I think, and you get interference, which becomes harder to deal with. First of all having a pressure drop across the throttle plate would make your 2 separate waves end up with very different amplitude (not to mention overall decreased maximum amplitude), and it would be a much more difficult task to compute the way it behaves. Not that it can't be done, but...

Oh and I just realized, this explains why some people say certain intakes make more noise. If the intake is either tuned well (high pressure zone of wave hits intake valve on time) or very poorly (low pressure zone hits intake on time, high pressure gets reflected back), this will create noise. So my guess is the reason stock intakes don't perform well is not because of restriction, but because the manufacturer wants to tune it so the pressure is as close to atmospheric as possible and that the air flows more continuously instead of in pulses, thus reducing noise.