Quadratic Residue Diffuser
Introduction
Diffusion in Acoustics is
the even spreading of sound energy in a given environment. The purpose of sound
diffusion is to even out the live and dead spots in a room where waves would
continue to reflect upon their same paths. A Diffuser reflects sound in an even
and predictable manner unlike a room with hard reflecting surfaces which would
not do this. A Diffuser does not remove sound energy but radiates the sound
energy in many directions leading to a live sounding space. One of the widely
used diffusers is the Quadratic Residue Diffuser (QRD).
The N7 Diffuser
An N7 QRD (with 7 wells)
has the following sequence 0, 1, 4, 2, 2, 4, 1. The deepest well is the well
with sequence ‘4’ and the shallowest well is the well with sequence ‘0’. The
deepest well value can be chosen in the design stage which further limits on
the lowest diffusible frequency. As the well position ‘0’ leads to a residue of
‘0’, the well depth is also ‘0’. This is true for diffusers of any order (N5,
N7, …). So, either the well ‘0’ is left as it is or it is split along the edges
as shown in Figure.1. RPG Acoustical systems, a well-known manufacturer
of QRD N7 diffuser, splits the ‘0’ well along the edges.
Figure 1 RPG QRD-734
QRDude Calculations
Let us consider an N7 QRD
with maximum well depth to be ~97mm which translates to a design frequency of
~1000Hz. The goal is to find out what is the difference between the well ‘0’ on
one side of diffuser making it unsymmetric versus splitting the well ‘0’ along
edges making it symmetric.
Figure 2 N7 QRD unsymmetric well
distribution
Figure 3 N7 QRD symmetric well distribution
Observations
There is no significant
change observed by leaving well ‘0’ as it is on one side or splitting it along
edges. Also note that if well ‘0’ were to be neglected for some reason, the
diffuser still needs an ‘End Fin’ on both sides to make it meaningful and in
this process one has just ‘added’ the split well ‘0’ approximately on both
sides!
QRD Video
To learn in depth about
QRD, please watch the video on YouTube by clicking the link below:
