Perforated Panel Absorber


In acoustically treating a room, there are a number of ways to overcome issues and achieve good sound. Absorption is one of these techniques, and constructing panels that will absorb from approx 250Hz and up is relatively easy to do, however it is the frequencies below 250Hz which prove to be challenging. This is where the perforated panel absorber can be useful.

Background
A perforated panel absorber is a resonating absorber - ie, it is 'tuned' to a frequency.

Physically, it is a box, where one side of the box has gaps in it where air can move in and out of the box. The other 5 sides of the box are solid and complete, with no gaps. If you build a six sided sealed box and drilled a hole in one side, that would be a perforated panel absorber. The name comes from the fact that one panel is perforated.

The idea of these 'gaps' is an important one, because the shape of these gaps does not matter at all. You can drill holes, you can have thin slots, you can have any shape you like!

The thing that matters is the percentage of the panel that is gaps.
If you have a panel that is 100cm2 and you drill a hole in it that is 1cm2 then 1% of the panel will be a gap, and 99% of it will be solid.

How to work out the size of the box
The box can be any size and shape you like. However, the size of the box does affect the tuning of the box, so (for instance) you won't be able to build a box that is 10cm deep, but will be tuned to 20Hz.


Panel width [cm]
Panel height [cm]
Panel thickness [cm]
Depth of the air space [cm]
Hole diameter [cm]
Amount of holes


Panel area [m2]
Volume Absorber [Liter]
Percentage of perforation [%]
Resonant frequency [Hz]


Formulas (taken from the Master Handbook of Acoustics)


for absorbers with holes:

Freq = 200 x square root of (P/(D x T))

where:
P = perforation percentage (eg, 5%)
D = depth of air space (in inches)

T = PT + 0.8 x HD

where:
PT = panel thickness (in inches)
HD = hole diameter (in inches)
  for absorbers with slats:

Freq = 216 x square root of (P/(D x PT))

where:
P = perforation percentage (eg, 5%)
D = depth of air space (in inches)
PT = panel thickness (in inches)

Notes:

the depth of the air space is the internal depth of the box, the distance from the inside of the panel with the holes/slats to the inside face of the rear panel. The panels themselves are not meant to move at all, therefore you should make them out of a material sufficiently thick so they don't move. Don't use 6mm MDF! If you're going with < 16mm MDF then you might like to put in a couple of braces - nothing ridiculous, just to stiffen the panels up a bit.

Bandwidth

Now we know how to tune the box to a particular frequency, but how wide a frequency range will it absorb?
The answer is: not very much. However, if we put stuffing inside it, then it will absorb a much wider range of frequencies.

The graphs in the book show that at the tuning frequency the absorption is very close to 100%, but if we take 80% as being our goal, then it will do roughly one octave either side of the tuning frequency.
ie, if we build a trap that is tuned to 50Hz, then we will get about 80% or more absorption between 25Hz and 100Hz.

Stuffing can be anything you like, but fibreglass is the cheapest and most effective performer, so that is what people normally use. Be warned though, fibreglass is nasty stuff, and so you should wrap it in fabric to ensure the fibres don't go everywhere!

Size of trap and absorption

These traps are not magical devices - they don't 'suck' bass from a room. They simply behave in such a way that lots of the bass frequencies that go into the trap (through the gaps in the front panel) don't come out again.
The key concept here is that if you build a bass trap that has a front panel size of 1m x 1m it will absorb a lot more bass than a box 10cm x 10cm with the same tuning frequency.

Guidelines
The trap becomes more effective at absorbing bass the more easily that the sound can get into the box to be absorbed. ie, a 1m2 box with 1% of the front panel open will be less effective than a 1m2 box with 5% of the front panel open, simply because there are more holes to let the sound in!
You will now realise that if you want to tune your trap for low frequencies, you can either make it have less holes, or be deeper. The guideline would be to keep the perforation percentage above 1%.

An example - My system
I own some panels that absorb from approx 250Hz up, so I wanted to complement these with absorption from 250Hz down.
Taking the idea that a trap is >80% effective over a two octave range, I decided to build two different tunings, one at 120Hz and one at 60Hz.
The 120Hz trap would absorb up to 240Hz and down to 60Hz with greater than 80% effectiveness.
The 60Hz trap would absorb up to 120Hz and down to 30Hz with greater than 80% effectiveness.
Combined, they should be effective over a range from 30Hz to 240Hz.

I decided that I would build my traps from a commonly available size of wood so I didn't have to do as much cutting, so the front panel of the traps are 900x600. So, using the above formula, using the tuning frequency as a goal, I calculated a trap that was ~30cm (12in) deep (the internal depth) and had a 3.6% perforation percentage with 1cm (0.4in) diameter holes and a 12mm (0.5in) thick front panel. This gives me the 120Hz I wanted.

So, what does 3.6% perforation actually mean?
Given that each hole has a surface area (using pi*r*r) 0.785cm2, and that the total area for the front panel is approx 5031cm2 (remember the front panel is 576mm x 876mm on the inside of the box) that means we need 230 holes.
These holes should be spread pretty evenly over the front face of the box, although you don't have to be super accurate with this - as long as they're relatively even. If we had a grid that was 12 rows by 19 rows of holes, that is 228 holes, which is easily close enough to 230, and it gives us a shape that matches the dimensions of the box. Holes would be in a grid with 4.5cms between the centres of the holes.

The same approach was used to determine the 40Hz traps.. which would end up being 0.85% perforation percentage, the same depth, and a grid of 6 x 4 of the 1cm diameter holes with a distance of 12.85cm between hole centres.

You will note that I used a perforation percentage under 1% for this trap, but I did so because I didn't want to make these traps any deeper than the other ones. I came up with this depth because it is the depth of my bookshelves, and so when I put the traps next to my bookshelves they don't stick out, but actually look rather neat - giving the bookshelves a 'recessed' appearance.
I also build two of each trap (4 in total) so I can put the traps symmetrically on each side of the room. I'm not sure if this matters much, but it fits in with my room layout, and gives twice the absorption of a single trap of each size. They can also be stacked to be 600 wide and 1.8m tall, or 900 wide and 1.2m tall, providing a handy shelf. I am about to build some subs (stereo) and will make these about 600 x 750 x the same depth. This will mean I can slot them under the absorbers and they will take up no additional floorspace, despite being quite large subs. This modular design is fantastic for my needs.
I filled my traps with fibreglass wrapped in the cheapest fabric I could buy, this will stop the fibres coming through the holes into the room.
I made the front face out of 12mm ply and after drilling the holes (LOTS of holes!) varnished them. They look ok, but if I did it again I would use MDF and paint them cream so they blend into the walls. Also, the fabric is a light colour and you can see it through the holes, which makes it look a bit strange with the varnished dark plywood.




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