How it works
The well depths follow a quadratic-residue sequence — for a prime number of wells N, the depth of well n is set by `n² mod N`. That specific pattern is what spreads reflected energy evenly across a wide fan of angles instead of beaming it back as a single echo. Fresnelcut uses the Schroeder grating relation, not the hobbyist quarter-wave shortcut, so the depths match published references.
Every well shares one width W and the fins share one thickness. Pick a lower design frequency and Fresnelcut solves the depths; the panel keeps working up to roughly `c / (2·W)` before the wells get wide compared to the wavelength.
When to reach for a QRD
A 1-D QRD scatters in the plane perpendicular to its fins. Mount the fins vertically and it spreads sound left-to-right — ideal behind a listening position or on side walls at the first reflection points. For scatter in both axes, step up to a 2D QRD or a skyline diffuser.
Worked example: N = 7 at a 500 Hz design frequency
Pick N = 7 wells and a design frequency f₀ = 500 Hz. The wavelength at 500 Hz is λ₀ = c/f₀ ≈ 343.2 / 500 = 0.6864 m, so the depth step is u = λ₀/(2·7) ≈ 49.03 mm. The residues `n² mod 7` for n = 0…6 are `0, 1, 4, 2, 2, 4, 1`, so each well's depth is its residue times u:
| Well n | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|---|
| Residue sₙ | 0 | 1 | 4 | 2 | 2 | 4 | 1 |
| Depth (mm) | 0.0 | 49.0 | 196.1 | 98.1 | 98.1 | 196.1 | 49.0 |
The deepest well is 196.1 mm — that's the stock thickness this particular panel needs. With a well width W = 25 mm the panel also reaches up to `f_high = c/(2W) ≈ 6.86 kHz` before it starts acting like a flat plate. Open this exact panel in the designer to see it previewed and get the cut file.
Stock, kerf, and what you'll need to build it
A QRD is one piece of stock deep enough for the deepest well, plus a backer if you're routing pockets rather than through-cutting each well. Deeper design frequencies need noticeably thicker stock — halving f₀ roughly doubles every well's depth — so most DIY builds sit in the 300–800 Hz range, where the deepest well lands somewhere around 120–330 mm depending on N. Fresnelcut's cut list accounts for kerf on both the wells and the fins, so the fin thickness you design with is the fin thickness you get; make sure it clears your laser or router bit with margin before you cut a full sheet.
QRD vs. its cousins
If a QRD's main weakness — a residual echo straight back toward the source — is the specific problem, a 1D PRD uses a different sequence to notch that reflection out. If reflections arrive from more than one plane (a ceiling cloud, a wide rear wall), a 2D QRD or skyline scatters both axes instead of one. For a full side-by-side, see QRD vs PRD vs skyline.
s_n = n² mod N, d_n = s_n · λ₀ / (2N)N = prime well count, λ₀ = wavelength at the design frequency f₀. Deeper wells come from larger residues.
Best for
- First-reflection points on side walls
- Rear-wall treatment behind the listener
- Rooms that sound harsh or echoey in the mids and highs
Not the tool for
- Low-frequency boom or boominess (use an absorber instead)
- Situations needing even scatter in both directions (use 2-D)
Start from a common size
N is the number of wells (a prime). More wells scatter more smoothly but make a wider, deeper panel. Pick one to open the designer pre-set: