The Diffuser Array

While the walls were being finished I began to design and build one of the studio's major acoustical elements, specifically the array of reflection phase grating diffusers that make up a large part of the main recording room's largest wall. I'd read a fair bit, both in Everest's book and on the net, regarding the advantages of this type of diffuser and was sold on the idea of making it a major part of the room treatments.

There are several major types of diffusers, each with their own strengths and weaknesses. I decided on the diffraction grating design, based on their efficiency over a broad frequency range and because they looked fairly straight forward to build. The idea is that by creating a set of grooves at various depths you can alter the phases of the scattered sound so that it can be constructively scattered in many different directions, essentially making the intensity of the reflected sound equal in the plane perpendicular to the grooves. There is an additional benefit from the fact that reflection phase grating diffusers also provide low-frequency absorption at frequencies below their useful diffusion limit. While commercially available grating diffusers are readily available (most notably from RPG Systems), they are quite expensive, running $700 or more per element for the root-19 design I'd settled on. It was late January of 2003 and I was already out of money, so I was resigned to the task of building them myself, something that became a recurring theme.

The particular style of grating diffuser I chose, called a quadratic residue diffuser, is basically a series of either vertical or horizontal "wells", whose depths are determined by a simple mathematical sequence - the quadratic residue sequence:

d = n² modulo p

where p is a prime number, and n is the series of integers from 1 to p.

Based on my desire to get the most out of every sheet of wood product (plywood and chipboard) I settled on a maximum well depth of 16 inches. Since 1x3 pine was relatively inexpensive I chose 2.5 inches as the cell width. The cell dividers were made from 7/16-inch chipboard, and the outer "shells" from 1/2-inch plywood. All these decisions resulted in diffuser elements which were 48 inches tall, about 55 inches wide, and 16 inches deep.

Half way through building the first root-19 element I understood why they are so expensive. They are a total pain in the ass to build and require a surprising amount of material. Despite my frugal choices each element cost almost $100 in materials alone. Each element weighs well over 200 pounds; I literally cut wood for days creating a huge mound of sawdust and acquired a large number of slivers.

Once the pieces were all cut they were assembled using wood glue, construction adhesive, and screws. Lots of screws! You can pray to whatever deity you wish, but while assembling these monsters I was bowing at the altar of whoever invented the cordless dirll!

The entire array includes 5 root-19 diffusers set vertically, and six root-7 diffusers set horizontally, also with 2.5 inch wide wells. Once these were finished I decided to build another root-19 array, this time only 12 inches deep, which would sit at the back of the control room. The middle picture shows the array in the main room, about three quarters complete. Another layer of the root-7 horizontal diffusers rests on top, flanking a single vertical root-19 diffuser.

The final picture shows the completed array in the main recording room receiving its coating of paint. The space under the lower diffusers is used as a cable race.