Quote:

I think it is needed to distinguish between a definite volume with a definite hole in it - and a kind of “wall-helmholtz” where the slits and depth are defined. Two total different things in practice.

It's the exact same principle, actually. The same equations apply to all forms of Helmholtz Resonator: they are all derived from the same underlying basis. It's just a simple mass-spring system, where the "mass" is the air trapped in the neck of the device, along with the mouth correction factor (A.K.A. "end correction") applicable to each specific case, and the "spring" is the air behind that. The only thing that changes between implementations, is the method for calculating the mass of the air "plug" in the neck of the device, and the method for calculating the resilience of the air spring behind.

For example, the equation for perforated panel is very similar to the one I already gave for slats:

fo = 200*sqrt( p / (t + (d*0.8))*(D) )

p = perforation percentage (percent open area)

t = panel thickness, in inches

d = hole diameter, in inches

0.8 = mouth correction

D = cavity depth, in inches

(Taken from MHoA)

That works for one hole or one thousand holes.

Not too meany people that I know of build tuned studio Helmholtz resonator traps as one single hole in one single enclosure. That's wouldn't be very effective for dealing with modal issues, for example: You need a much larger effective area than can be obtained from a single hole, and a much larger volume than can be obtained from a single enclosure. That's how the basic theory is usually explained, since it it easier to understand like that, but in real-world studios the actual implementations in treatment devices are usually either perforated panel or slot walls.

The general form of the equation for all such devices is in the image below.

- Stuart -