The depth formula
Each well's depth is its quadratic residue times a fixed step. The step is the wavelength at your design frequency divided by twice the well count:
d_n = s_n · λ₀ / (2N), where λ₀ = c / f₀ and s_n = n² mod NA worked example
Take a QRD with N = 7 wells at a design frequency of 500 Hz. The wavelength is about 686 mm, so the depth step is 686 / 14 ≈ 49 mm. The residues `n² mod 7` for n = 0…6 are 0, 1, 4, 2, 2, 4, 1 — giving depths of 0, 49, 196, 98, 98, 196, and 49 mm. The deepest well is about 196 mm, which is what your stock has to accommodate. Open this exact 7-well, 500 Hz panel in the designer to see it previewed and get the cut list.
Design frequency vs. depth, at a glance
Well depth scales directly with wavelength, so it climbs fast as the design frequency drops. Holding N = 7 wells fixed (the most common starting point) and varying only the design frequency:
| Design frequency f₀ | Depth step (u) | Deepest well |
|---|---|---|
| 1000 Hz | 24.5 mm | 98.1 mm |
| 800 Hz | 30.6 mm | 122.6 mm |
| 500 Hz | 49.0 mm | 196.1 mm |
| 300 Hz | 81.7 mm | 326.9 mm |
| 200 Hz | 122.6 mm | 490.3 mm |
Two things fall out of that table. First, deep bass is expensive in stock: reaching down to 200 Hz needs a deepest well pushing half a metre, which is why diffusers are a mid/high-frequency tool and boom is an absorber job. Second, well count has a smaller effect on the deepest well than most people expect — moving from N = 7 to N = 17 at the same 500 Hz only changes the deepest well from about 196 mm to about 323 mm (17's largest residue is a bigger fraction of N), not a small one; it's the design frequency, not the well count, that mainly drives depth.
Working backwards from your stock
More often the constraint runs the other way: you have material of a certain thickness and want to know how low the panel will reach. The deepest well can't exceed your stock, so a shallower panel simply has a higher design frequency. Fresnelcut solves this for you — set the maximum depth and it reports the achievable f₀.
f₀ = s_max · c / (2N · d_max)