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Panel Resonator - Helmholtz Panel Resonator - Slot Resonator

Placing the Traps - Skyline Diffusor

Quadratic Residue Diffusor (Size)

- Quadratic Residue Diffusor (Design frequency)

How to build a contact microphone - Links

There are two commonly used traps, both of which are easy to build. They are the panel Resonator and the Helmholtz resonator. However, to be successful you first have to know precisely where your problem frequencies are and then you have to build these traps accurately to ensure that they work at the right frequency.
Both types of Resonator take up a large area, but have the advantage of being only a few cm deep. Even so, you must bear in mind that these are tuned traps and so are normally used to reduce specific resonances. They are not suitable for use as broad-band Resonators, with the exception of a panel trap constructed with a highly damped, limp membrane.

A Helmholtz resonator is simply a box with a port on its front side to couple the enclosed volume of the airspace in the box to the air in the room. The depth of the enclosed airspace in the box behind the port and the width and depth of the port control the resonant frequency of the bass trap.

Another form of helmholtz resonator is created using perforated plywood - i.e. plywood with hundreds of holes in it. You see it in hardware stores holding up tools etc. If you place a panel of this over an air cavity like in a panel resonator not only do the little holes act like bottle necks the whole panel acts as a low frequency panel resonator!

Standing waves occur at harmonics of the fundamental frequency - that is 2, 3, and 4 times the fundamental. Thus a room with an 2.45 meter ceiling has standing waves forming at 70 Hz (the fundamental frequency or first harmonic), 140 Hz (the second harmonic), 210 Hz (the third harmonic) and 280 Hz (the fourth harmonic).
Rooms with smaller dimensions often have standing waves or resonance build ups that are very noticeable causing coloration at around 200 Hz.

The formula for determining the fundamental frequency of a standing wave for a particular room dimension is:

fo = V / 2d

where:
fo = Fundamental frequency of the standing wave
V = Velocity of sound (344 meter per second)
d = Room dimension being considered in meter (length, width and height)

The formula for determining f_res:

f_res = c/2 * sqrt( (l/lx)^2 + (m/mx)^2 + (n/nx)^2 ), with l,m,n = 0,1,2...

c = 344 m

Calculate resonant frequency, Bandwidth and Q from given Volume, Port- length and width.

Height:

Width:

Depth:

Volume

Liter

Port Length:

Port Diameter:

Calculated Port Area:

cm²

calculated resonant frequency:

Calculations are based on the American Institute of Physics Handbook, 1957 McGRaw Hill, Inc.

Bandwidth :

flow (f1) :

fhigh (f2) :

The internal damping of the resonator is thus determined by the quality, while the outside damping of the resonator is seized by the sound field (thus those effect actually which can be used) by the coupling relationship k:

k = 5 x 10^-13 x V x F x Q x f³

k = coupling relationship [ cm³/s³ ]
V = volume of the resonator [ cm³ ]
Q = quality
F = factor, which depends on the arrangement of the resonator in the area (applies only to single resonator)
f = frequency [ cycles per second ]

Free standing:

Against wall:

Room corner:

Usual values for k lie between 0.02 (for small increased heights) and 0,4 (for strong increased heights). Helmholtzresonatoren show largest effect thus in space corners.

A panel resonator is created when you place a sheet of plywood or fibreboard, with insulation glued to the back of it, over an air cavity. The panel will have a resonate frequency of its own, tap it and you will hear it. When it is placed over a sealed cavity, and insulation is attached to the back, everytime it hears its own note it resonates and the air in the cavity resonates and the insulation absorbs the resonance, hence absorbing the frequency! It is important to note that here we have an resonator that reflects the high frequencies and attenuates the low. With the hangers all that exposed insulation absorbs the high frequencies as well so the panel resonator has a place in the studio. The two factors determining the frequency of absorption are:

The mass or density of the panel.
The depth of the air cavity, i.e. depth of the sealed timber frame.

Calculate frequency of absorption of the Panel Resonator
Filling the cavity with fibreglass or mineral wool tends to lower the resonant frequency by up to 50 per cent as well as doubling the effectiveness of the trap. It also lowers the Q of the trap so that it is effective over a wider frequency range. A typical panel-type trap is effective for frequencies around one octave either side of the centre frequency, which at least has the advantage that you don't have to be absolutely accurate to get results.

Calculate depth of the Panel resonator

Calculate mass of the Panel

You can discover the resonant frequency by sticking a cheap contact mic on to the panel's surface, then plugging the mic into a preamp or mixer with a VU meter. Play a test tone from an oscillator or test tone CD using loudspeakers, and vary this around the frequency the trap is designed for until you get a maximum meter reading. This will be at the trap's resonant frequency.

How to build a contact microphone

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.

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.

Calculate Resonant frequency of Helmholtz Panel Absorbers with holes

The formula for calculating the Helmholtz resonant frequency for a slot resonator is:

WRONG often published and in calculators used formula

fo = 2160*sqrt(r/((d*1.2*D)+(r+w)))

CORRECT formula

fo = 2160*sqrt(r/((d*1.2*D)*(r+w)))

fo = resonant frequency
r = slot width
d = slat thickness
1.2 = mouth correction
D = cavity depth
w = slat width
2160 = c/(2*PI) but rounded
c = speed of sound in inch/sec

What is this mouth correction?

A Helmholtz resonator is a mass-spring system, which is comparable with a panel or membrane resonator.
The system is based on a mass which vibrates in resonance on a spring.
The ratio of the mass versus the dynamic stiffness of this spring defines the resonance frequency.
The air layer in the cavity acts as a spring with a certain dynamic stiffness mainly defined by its volume.
The larger the Volume, the weaker the spring becomes (lowering resonance frequency) and vice versa.

For a panel resonator it's easy to imagine what the mass is: the panel.
The heavier this mass becomes the lower the resonance frequency and vice versa.
As such a panel resonator is mainly defined by the combination of both properties.
This isn't complete, since angle of incidence, weakness of spring, damping etc. will influence the resonance frequency and the Q-factor.

For a Helmholtz resonator this mass is represented by the mass of the air enclosed by the neck or slot of the resonator.
However this apparent mass extends outside the exact geometrical boundaries of this neck or slot.
This is covered by the mouth correction, which is in fact a correction factor increasing those geometrical boundaries.
In reality this phenomenon is much more complicated than the simple factor, used by the traditional formulas.
As such the distance between those necks or slots (interaction) and others will influence this correction.
For practical use however the standard formulas are a good approach.

If the gaps vary say 5mm, 10mm, 15mm, 20mm and the wall is angled as shown below, a broad band low mid resonator is created that still keeps the high frequencies alive.
Remember the cavity behind must be airtight!

By working out the different slat widths and slot gaps you can create a broadband low mid resonator at specific frequencies.

Download here the Excel - Slot Helmholtz Resonator