AudioCalcs
Diffuser Calculator — QRD Well Depths
Calculate QRD diffuser well depths from prime number sequence for a target frequency range.
How We Calculate This
QRD Sequence
s(n) = n² mod N (where N is the chosen prime number)
Well Depths
Depth(n) = s(n) × wavelength / (2 × N)
The wavelength is calculated from the design frequency and speed of sound. Each well depth creates a different path length, scattering reflected sound evenly across a wide angle.
Frequency Range
Upper limit = c / (2 × well width) — set by how narrow each well is.
The "design frequency" here is the depth-quantum reference that sets the well-depth steps, not literally the lowest diffused frequency. Useful scattering extends roughly one octave below it (down to about half the design frequency), so the lowest effective figure is reported as f₀/2.
Genuine low-frequency diffusion also needs the panel period width to be at least one wavelength of the lowest frequency you want to scatter. A single short period (for example seven 40 mm wells = 280 mm wide) is only one full wavelength wide at ~1.2 kHz (c/0.28 m ≈ 1225 Hz), so below that the panel is too narrow to diffuse properly — use a double or triple period to actually scatter the lower end of the stated range.
Frequently Asked Questions
N=7 is the most common choice, giving a good balance of diffusion quality and construction complexity. N=5 is simpler but less effective. N=11 or N=13 provide better diffusion but require more wells and deeper maximum depth. Higher primes give wider bandwidth diffusion.
The design frequency is the depth-quantum reference that sets the well-depth steps, not literally the lowest diffused frequency. For rear wall studio diffusers, 1000-2000 Hz is common. Useful scattering runs from roughly half the design frequency up to c/(2w) where w is the well width. Lower design frequencies require deeper wells. Note the low end also depends on panel size: the period width must be comparable to the wavelength, so a single short period will not fully scatter the lowest stated frequency — use a double or triple period for genuine low-frequency diffusion.
Well width determines the upper frequency limit of diffusion. Narrower wells (30-40 mm) diffuse higher frequencies. The upper limit is approximately the speed of sound divided by twice the well width. Keep wells narrow enough that the highest frequency of interest is covered.
Yes. QRD diffusers are commonly built from MDF or plywood dividers with a solid back panel. The wells must be rigid and non-absorptive — hard, smooth surfaces reflect sound into the diffusion pattern. Paint or varnish the interior surfaces. Ensure accurate depth cutting for each well.
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Last updated: March 2026
All calculations are estimates based on standard formulas. Always verify results for critical applications.