Diffuser Design Calculator
Design a quadratic-residue diffuser (QRD): pick a prime number of wells and a design frequency to get the exact well-depth sequence, the high-frequency limit from the well width, the period size, and a depth diagram — or switch to a 2D Skyline block array.
ℹ These are the textbook Schroeder equations (dₙ = (n² mod N)·λ/2N), which give a sound starting design — but real diffusers are approximate: a finite panel diffuses less at the low end than the formula implies, periodic tiling causes lobing (optimised/modulated diffusers reduce it), and well dividers (fins) and build accuracy matter. A diffuser scatters sound to keep a room lively — it does not absorb, so use it where you want energy preserved (rear wall, or first reflections if you prefer scattering to absorption). Metric; everything runs in your browser.
How It Works
A quadratic-residue diffuser (invented by Manfred Schroeder) is a row of wells of different depths, separated by thin fins. The depths follow a number sequence that gives the reflected sound an almost-flat scattering pattern across a wide range of angles, so instead of a hard echo you get even, diffuse reflection. For a prime number of wells N, well n gets the depth dₙ = (n² mod N) · λₗₒₓ / (2N), where λₗₒₓ = c / fₗₒₓ is the wavelength at your chosen design frequency. The deepest well sets how low the diffuser still works; the well width sets the top limit, fₕₒₕₕ = c / (2·width), because once the wavelength gets close to a well’s width the wells stop behaving as designed. A 2D Skyline diffuser extends the idea to a grid of square blocks whose heights come from a 2D residue array ((x²+y²) mod N), scattering in both directions instead of just one.
The equations are exact, but a built diffuser is an approximation of the ideal. A panel of finite size loses low-frequency diffusion (you need enough periods), and tiling identical periods side by side creates lobing — concentrations of energy at certain angles — which modulated or optimised sequences are designed to avoid. Fin thickness, accurate well depths, and a rigid build all affect the result. Most importantly, a diffuser scatters energy rather than removing it: use it to keep a space sounding live and spacious (classically on the rear wall behind the listener), and reach for absorption when you actually need to reduce energy.