QRD Diffuser Calculator: Well Depths for N7, N11, N13, N17
Generate well depths for a 1D QRD, block heights for a 2D skyline, or an open/reflective binary amplitude sequence. Choose the surface type before entering dimensions.
Well depth sequence
| Well index n | Residue | Depth (cm) | Filler (cm) |
|---|---|---|---|
| 0 | 0 | 0.0 | 19.6 |
| 1 | 1 | 4.9 | 14.7 |
| 2 | 4 | 19.6 | 0.0 |
| 3 | 2 | 9.8 | 9.8 |
| 4 | 2 | 9.8 | 9.8 |
| 5 | 4 | 19.6 | 0.0 |
| 6 | 1 | 4.9 | 14.7 |
Filler thickness raises each floor inside a box built to the deepest well. Width includes N clear wells and N + 1 equally thick fins/cheeks. Add any extra case separately.
2D residue grid and block heights
Block cut counts
| Residue | Height (cm) | Positions |
|---|
Heights project outward from a common base; zero means bare base. Blocks abut without fins or gaps. Dimensions exclude backing and frame. This grid supplies geometry, not a predicted polar response.
Binary amplitude sequence
1 = reflective cell; 0 = opening over an absorber. Keep the sequence order.
This is one row of equal-width cells. Open share assumes equal cell areas and is not an absorption coefficient. Specify mask thickness, backing and any two-dimensional folding separately; a checkerboard or an arbitrary row wrap is not the same design.
What a quadratic residue diffuser is
A QRD uses a sequence of unequal well depths to vary the phase of reflected sound across a surface. It is designed to redistribute reflection. For what a quadratic residue diffuser is and how its sequence changes the angular response, read the theory guide. The dimensions here use an ideal rigid-surface model.
How the dimensions are calculated
In 1D QRD mode, s(n) = n² mod N and depth = s(n) × c / (2Nf₀). Sound speed is fixed at 343 m/s. The round trip into and out of a well supplies the factor of two. The N7, N11, N13 and N17 depth tables and formula show the worked values.
The well-width estimate c / (2w) marks a limit of the simple plane-wave model. Ideal phase repetition occurs at N × f₀, when the well returns line up again. Neither figure certifies a continuous working band, and f₀ is a design input rather than a measured low-frequency cutoff. Read the math behind these numbers for the phase and polar-response explanation.
Skyline mode uses s(row, column) = (row² + column²) mod N and height = s × c / (2Nf₀). For N7 at 500 Hz, its largest residue is 6 and tallest block is 29.4 cm. Abutting 3.8 cm blocks make a 26.6 cm square period before a frame. Reversing the surface from wells to projecting blocks changes the phase sign; real scattering still depends on the complete geometry.
BAD mode uses maximum-length binary sequences generated from an all-ones seed. The recurrences are s(i + 3) = s(i + 1) XOR s(i), s(i + 4) = s(i + 1) XOR s(i), and s(i + 5) = s(i + 2) XOR s(i). These produce periods of 7, 15 and 31 cells. The sequence does not use a QRD design frequency or well depth.
The types of acoustic diffusers comparison explains the different surfaces. For a well-panel cut list, see how to build a QRD diffuser. Start with absorption versus diffusion if the treatment's purpose is still undecided.
Sources and limits
The phase-grating model is covered in Schroeder Diffusers: A Review. The two-dimensional residue construction is described in the quadratic-residue array patent. The planar binary amplitude diffusor patent describes an MLS pattern combining reflective and absorptive regions.
ISO 17497-2 specifies directional diffusion measurement. This calculator generates dimensions and sequence values; it does not measure diffusion, absorption, mounting capacity or minimum listener distance.
Frequently asked questions
What does the QRD diffuser calculator calculate?
The 1D QRD mode calculates well depths and filler thicknesses for N7, N11, N13 and N17. It also gives period width, a well-width frequency estimate and the ideal phase-repetition frequency. These are calculated geometry, not measured acoustic performance.
What depth are N7 wells at 500 Hz?
With sound speed set to 343 m/s, the depths are 0, 49, 196, 98, 98, 196 and 49 mm. Depth is measured inward from the common opening plane; backing and mounting space are extra.
Can this calculate a 2D skyline diffuser?
Yes. Skyline mode uses (row squared + column squared) modulo N to produce an N by N residue grid, block heights and counts. Period width is N times the block width for abutting blocks, excluding an outer frame.
How does the binary amplitude diffuser mode work?
BAD mode generates a maximum-length binary sequence of 7, 15 or 31 cells. One denotes a reflective cell and zero an opening over an absorber. It reports the sequence, open-cell share and strip width; it does not predict absorption or diffusion coefficients.