Diffusion Calculator — QRD & PRD Diffuser Design

The QRD well-depth sequence is calculated using:

depth_n = (n² mod N) × v / (2 × N × f)

Where n is the well number (0 to N−1), N is a prime, v is the speed of sound (343 m/s at 20°C), and f is the design frequency. The deepest well corresponds to the largest residue in the n² mod N sequence — for N=7 the residues are [0,1,4,2,2,4,1], so the maximum is 4 (not N−1=6).

Well width = v / (2 × N × f)

A Primitive Root Diffuser (PRD) instead uses depth_h = (g^h mod N) × v / (2 × N × f) for h = 1 to N−1, where g is a primitive root of N (so g^h cycles through every residue 1…N−1 exactly once). This gives N−1 wells with no flat zero-depth well.

The effective bandwidth runs from the design frequency up to roughly N times the design frequency (the high-frequency limit set by the well width, f_high = v / (2 × well width)).