How to Build a QRD Diffuser: Cut List and Depths

A quadratic residue diffuser is one of the few pieces of acoustic treatment where the design work is harder than the build. Once the depth sequence exists, the panel is a shallow box with dividers in it, and the tolerances that matter are far looser than woodworking instinct suggests. This walks through a complete seven-well panel, then through the reasons a correctly built one can still do nothing audible.

Fix the design frequency to the depth you can accept

Depth is almost always the binding constraint, so work backwards from it. A deepest well of 20 cm plus a back panel and a frame puts roughly 22 cm into the room, which is about as far as most people will tolerate on a rear wall.

At that depth an N7 device is designed at 490 Hz, an N11 at 702 Hz and an N13 at 792 Hz. Lower primes reach lower for the same depth, and the reasoning behind that, with tables for other depths, is set out in QRD diffuser well depths.

This build uses N = 7 at a 500 Hz design frequency, 3.8 cm wells and 6 mm fins. It is the configuration most domestic rooms should start with: shallow enough to hang, wide enough to tile two or three across a wall, and cheap enough in material that a first attempt is not painful.

For the phase model that explains the round-trip factor, read how the well depth formula is derived.

The numbers for this panel

Design wavelength at 500 Hz is 68.6 cm. The residue sequence for N = 7 is 0, 1, 4, 2, 2, 4, 1, and each depth is that value multiplied by 68.6 and divided by 14.

Well	Residue	Depth	Filler block thickness
1	0	0.0 cm	19.6 cm
2	1	4.9 cm	14.7 cm
3	4	19.6 cm	0.0 cm
4	2	9.8 cm	9.8 cm
5	2	9.8 cm	9.8 cm
6	4	19.6 cm	0.0 cm
7	1	4.9 cm	14.7 cm

The filler column is the practical part. Rather than building seven boxes of different depths, build one box with an internal depth of 19.6 cm and raise each well floor with a block. The blocks do not need to be solid; a rigid offcut screwed or glued flat to the back panel is enough, provided it seals well enough that the well behaves as a closed cavity of the stated depth.

Period width is 7 wells at 3.8 cm plus 8 fins at 6 mm, which is 31.4 cm. Panel height is free; 60 cm is convenient from a standard sheet and keeps the finished object liftable by one person.

Cut list

For one panel, 31.4 cm wide, 60 cm tall, 19.6 cm internal depth:

• Back panel, 18 mm ply or MDF: 31.4 x 60 cm, one piece
• Sides, 18 mm: 19.6 x 60 cm, two pieces, plus top and bottom at 31.4 x 19.6 cm if the box is fully closed
• Fins, 6 mm ply or hardboard: 19.6 x 60 cm, eight pieces
• Filler blocks: one at 19.6 cm, two at 14.7 cm, two at 9.8 cm deep, each 3.8 x 60 cm in plan. Wells 3 and 6 are the full depth of the box and take no block
• Fixings, wood glue, and a cleat or French cleat sized to the finished mass

The two outermost fins form the inside faces of the side walls, so a box made from 18 mm material with 6 mm liners on the inside faces gives the correct first and last well widths without any special joinery.

Build order and the tolerances that matter

Cut the fins from a single sheet in one setup so their depth is identical. Uneven fin depth shows up as a visibly wavy face, and it is the one dimension that is worth being fussy about.

Mark the fin positions on the back panel before assembly, spacing them 3.8 cm apart with the fin thickness included, and dry fit the whole set before glue touches anything. Grooves cut with a router or a table saw make the assembly self-aligning. Butt joints with glue blocks also work and cost nothing in performance.

Fit the filler blocks first, then the fins. Working the other way round leaves seven narrow slots to reach into.

The tolerance question comes up constantly. Well depth errors of a few millimetres are irrelevant at a 500 Hz design frequency, where the shallowest non-zero well is 4.9 cm and the wavelength is 68.6 cm. Sound entering a well travels the depth twice, so a 1 mm depth error is a reflection phase error of about one degree. Fin thickness and spacing matter more, because they set the well width and therefore the top of the working range, but even there a millimetre moves the upper limit by a few percent.

What genuinely matters is not dimensional accuracy at all. It is that each well is a rigid, sealed, non-porous cavity: no gaps at the edges of the filler blocks that let one well leak into its neighbour, no bare porous edge, and back and side panels stiff enough not to flex. The next section is why.

Why sealing matters more than accuracy

The single most cited measurement of a real quadratic residue diffuser is the cited 1992 reverberation-chamber study of an array of 48 N = 7 units. It reported absorption coefficients far higher than a rigid reflector would show, and the largest values sat below the lower limit of the design frequency, where the device was supposed to be doing nothing at all. Those units were built from 3 mm plywood well walls, a 6 mm plywood case and chipboard well bottoms.

Two things follow, and builders routinely take only the first.

Some absorption is inherent. A narrow, deep well is a quarter wave resonator, and near its resonance it loses energy to viscous friction at the walls. That loss rises as wells get narrower relative to their depth, which is a reason not to push well width below about 2.5 cm on a deep panel.

Most of the excess is not inherent. Subsequent work traced the very large coefficients in early measurements to the construction rather than to the phase grating: thin panels that flex, well bottoms of porous board, and joints that leak. A panel built from rigid, sealed, non-porous material absorbs far less than those figures imply. This is why the sealing advice above matters more than getting depths to the millimetre, and why chipboard or unsealed MDF at the bottom of a well is a worse choice than it looks.

Either way, a wall of diffusers is not acoustically equivalent to the bare wall it replaced. Budget for some absorption, and do not add diffusion to a room that is already too dead.

Finishing

Leave the wells open. Covering the face with fabric adds absorption exactly where the scattering happens, and stretching cloth over a diffuser turns it into a mediocre absorber with an expensive frame.

Paint is fine in thin coats, and on porous sheet goods a sealed surface is worth having for the reason above. A heavy build-up of paint or filler in a narrow well slightly reduces its effective width, which is harmless, but pooled finish at the bottom of a deep well changes its depth and is worth avoiding by finishing the components before assembly.

Mounting

Rear wall, behind the listening position, fins vertical for horizontal scattering. Centre it on the room axis if the wall allows, at a height that spans seated ear level.

Distance matters more than most builders expect. The scattered wavefront has to reform before it reaches the listener, and guidance in the literature is commonly expressed as several wavelengths of the design frequency between the device and the ears. At 500 Hz that is roughly two metres. A diffuser mounted 60 cm behind a chair is being used as an irregular reflector, which is not what the depth sequence was designed for.

Fix into structure, not into plasterboard alone. A box of this size in 18 mm material with filler blocks is heavy, and the failure mode is not subtle.

When two or more panels go up

Tiling identical periods edge to edge creates a periodic grating, and a grating concentrates energy into lobes at predictable angles instead of spreading it. The cited review discusses array modulation. Mirroring one QRD is not a reliable remedy because the sequence has cyclic symmetry; compare the intended array, including gaps and other surfaces, rather than assuming each added period improves diffusion.

Two or three periods across a rear wall is a normal, effective installation. Twelve identical periods in a row is a diffraction grating with a nice finish.

Why a finished panel can do nothing

The common failure modes, in the order they show up:

Nothing changed at all. The listening position is too close, the panel is too small relative to the wavelengths involved, or it is on a wall that was not producing a problem reflection. A single 31 cm wide period on a large wall is a small target; the energy that misses it is unaffected.

The room got brighter and harsher. A diffuser returns nearly all the energy that hits it, while the absorber it replaced returned almost none. If the room previously relied on broadband absorption for its tonal balance, swapping in diffusion changes that balance. The fix is to rebalance rather than to remove the diffusion: keep absorption at the first reflection points and let the rear wall scatter.

Imaging did not improve. Diffusion on the rear wall does not treat side wall and ceiling first reflections, which are the reflections that smear a stereo image. Those want absorption, and they want it before any diffuser goes up.

Low-frequency problems are unchanged. They will be. A 20 cm deep device cannot interact with a 5 metre wavelength. Modal problems are the job of porous absorption with depth, positioned in the corners, or of speaker and seat placement.

A buzz or rattle appeared. A loose fin or an unglued filler block in a resonant cavity is an excellent noise generator. Locate it by tapping the face rather than by re-measuring the room.

Related reading

The device type decision, if it is not yet settled, is covered in QRD vs skyline vs BAD panel diffusers. The full depth tables for other primes and design frequencies are in QRD diffuser well depths, the background on where diffusion belongs in a room is in how acoustic diffusers work, and the QRD diffuser sizer generates the depth sequence and panel width for any prime and design frequency.