Fresnelcut

Design

How deep should diffuser wells be?

Well depth is the number people fret over most, because it decides both how low the diffuser works and how thick a piece of stock you need. It's fully determined by two choices: the design frequency and the number of wells.

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 N
f₀ = design frequency (the low edge), N = prime well count, c ≈ 343 m/s at room temperature.

A 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.

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)
s_max is the largest residue. Halving your available depth roughly doubles the low-frequency limit.

Related reading

What is a quadratic-residue diffuser?A plain-English explanation of the quadratic-residue diffuser (QRD): what the wells do, why the depths follow n² mod N, and when to use one.QRD vs PRD vs skyline: which diffuser do you need?Compare the three main Schroeder diffusers — quadratic-residue, primitive-root, and 2-D skyline — and pick the right one for your room.

Design one now

1D Quadratic-Residue Diffuser (QRD)The classic well-and-fin panel that scatters horizontally.1D Primitive-Root Diffuser (PRD)A QRD cousin that suppresses the straight-back reflection.

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