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  Calculate Quadratic Residue Diffusor ( estimated design frequency )



Calculate here QRD (estimated Size)




The goal became to find a surface geometry which would permit designers the predictability of diffusion from MLS diffusers with a wider bandwidth.
The new system was again introduced by Schroeder in 1975 in a paper describing the implementation of the quadratic residue diffuser or Schroeder diffuser ? a device which has since been widely accepted as one of the de facto standards for easily creating diffusive surfaces.

Rather than relying on alternating reflecting coefficient patterns, this method considers the wall to be a flat surface with varying impedance according to location. This is accomplished using wells of various specific depths arranged in a periodic sequence based on residues of a quadratic function.

sn = n2 mod(p)

where sn is the sequence of relative depths of the wells, n is a number in the sequence of non-negative consecutive integers {0, 1, 2, 3 ...} denoting the well number, and p is a non-negative odd prime number.
For example, for modulo 17, the series is

0, 1, 4, 9, 16, 8, 2, 15, 13, 13, 15, 2, 8, 16, 9, 4, 1, 0, 1, 4, 9, 16, 8, 2, 15 ...

The actual depths of the wells are dependent on the design wavelength of the diffuser. In order to calculate these depths, Schroeder suggests the function

dn = sn * (DF / 2 p)

where dn is the depth of well n and DF is the design wavelength.

The widths of these wells w should be constant and small compared to the design wavelength
(no greater than DF / 2; Schroeder suggests 0.137 * DF)

 
Design frequency: Hz
Prime seed:  
 
Speed of sound: 344 m/s
Show sn 

Calculations for the Quadratic Residue Diffusor




Links:
Auralex
Primacoustics Razorblade Diffusor
Using RPG Diffusors to Enhance Room Acoustics
Silentsource
Technical Articles
Room Acoustic Active Diffusers
RPG Diffusor Systems


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Disclaimer
Please keep in mind that I am not an expert or an authority on acoustics, and the information presented here is just my opinion. I do however have many years of practical experience and my opinion is based on that. Please take this information for what it's worth and hopefully you will find it useful.