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Ok, so using the above equations we can calculate the dimensions of the diffuser. With a Diffuser designed to work at frequencies down to 1000 Hz the resulting sequence Is the same as the original sequence.

How to avoid the maths:

If you are not keen on maths you could use this freeware tool to do your calculations for you it is available from:  

http://www.subwoofer-builder.com/qrdude.htm the calculations can also be done online at:

http://www.mh-audio.nl/diffusor2.asp#calcul

The Calculations for the Quadratic Residue Diffuser are sound in this app are sound, they have been compared to the calculations above. It is fairly safe to assume that the rest are good as well.  

When designing any acoustic treatment it is important to consider the types of materials are going to be required for the construction. Again as with any design it is always a trade off between  cost and effectiveness. The best material for the construction of the QRD diffuser  is MDF, MDF is both dense enough and cheap enough.
This image shows how positioning shelving on the rear wall in front of your monitors to act as a diffuser or deflector can help with acoustics, When sound waves reach the unit, they are scattered.
Screen shot from QRDude a freeware acoustic design tool.
The Top View of a Schroeder Diffuser 1000 Hz
16cm
81.6 cm
4.7 cm
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Here you will Learn how to construct your own Quadratic Residue (Schroeder)  Diffusers. Learn some of the maths involved in their design. And how it is applied. Also get plans and advice on placement.

The Theory

There are many different ways to diffuse sound waves. One of the most simple is to use a book case full of books, the different depths of the books work in a similar way to quadratic residue diffusers. Books are one method but they are obviously not as effective as a diffuser with specific dimensions designed to perform at critical frequencies.  

A diffuser works by scattering waves in different directions preventing them from reflecting straight back on the path which they came. This is desirable because it can help to combat some of the acoustic problems it causes. The problems a diffuser can help to combat are, standing waves, and cancellation problems. Diffusion can also help with flutter echo's.

Diffusion and absorption can help to combat similar phenomena, but the main advantage of diffusion over absorption is that it can make a space feel much larger than it actually is. Essentially what a diffuser does, is to push the walls further away. Improving the sound of the room with out making the room sound boxy.
The diffuser design here is based on quadratic number theory, basically this is a sequence of numbers based on a prime number, the reason that this number sequence works so well is because it has a random quality, and the results are approximate to quarter wave lengths which helps with its effectiveness. These diffusers are also known as Schroeder diffusers. Diffusers have an effective bandwidth of 4 octaves. This type of diffuser is effective on a 1 dimensional plane, in some applications it may be better to use a skyline diffuser which can diffuse sound coming from the side as well as the front (2 dimensional).

The sequence for the prime number 17 is:

0, 1, 4, 9, 16, 8, 2, 15, 13, 13, 15, 2, 8, 16, 9, 4, 1
Before a diffuser can be designed its lowest frequency must be chosen. With diffuser design it is all ways a trade off between the frequency, and the cost of construction. The lower the frequency the higher the cost of construction. This is because for the diffuser to be effective at lower frequencies it has to be larger, the wells have to be deeper which means using more materials.

 Ok so having chosen the diffusers critical frequency the next stage is to ascertain the frequencies wave length. This involves some simple calculations, yes sorry it is impossible to talk about diffuser design with out going in to at least some maths.
The Maths:

There are two main components which have to be calculated when building a QRD:
The Well Width:

To calculate the wave length we must divide the velocity of sound in air (m/s) by the frequency in (Hz)

Velocity, in air, at 20°C = 343m/s
Frequency = 1000Hz
Wavelength (λ)





Λ = 0.343m or 34.3 cm

The well width is then calculated as:

17.15 x 0.137 =  4.7cm
The Well Depth:

To calculate the well depth we must use the calculation below





N= the prime number
modn = the residue number
Λ = wavelength
Dn = well depth / number

The resulting sequence (cm) is:

0, 1, 4, 9, 16, 8, 2, 15, 13, 13, 15, 2, 8, 16, 9, 4, 1 (rounded)
The next stage for was to calculate how much wood was required for the construction. MDF comes in sheets which are 1220mm x 2440mm and Can be of a different thickness. The closest I could get to 4.7cm thickness was to get two sheets of 18mm and one of 12mm making 4.8cm thickness when placed together.  The 1220mm will be used as the height of the diffuser and then just cut it in to lengths then glue the lengths together.

It was easy to work out how much wood is needed, just subtract each number from 16 then, add all of the numbers together to give a total length.

    16- 0   = 16
    16- 1   = 15
    16- 4  = 12
    16- 9  =  7  
   16- 16 =  0
   16- 8  =  8
    16- 2  = 14
    16- 15 = 1
    16- 13 = 3
    16- 13 = 3
    16- 15 = 1
    16- 2 = 14
    16- 8 =  8
    16- 16 = 0
    16- 9 =  7  
   16- 4 = 12
    16- 1 = 15  



Giving a total of = 136 cm (with this in mind there is scope to build another 2000 Hz diffuser using the same wood) your local timber merchant should be able to cut the wood to the right length for you for a small fee.

Obviously some sort of fixing method is required to build the diffuser. Make two ends, one for the top and one for the bottom. Screw the top end first then screw the bottom on. This is a cheap but effective method for construction. Dowels would be an alternative but its what ever you feel comfortable with. Being used to working with screws made this the first choice. It is important to block the ends with wood as this forms a cavity for the sound. Essentially what you are doing is building a book case, with out the books.

As soon as the  diffusers are finished  they'll be some images to view of the construction process.
You should also check: A DIY Approach for more info
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1220mm
2440mm
1360mm
Sheet of MDF
Diagram Showing the Cuts and the Required Wood
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flutter echo