Concert Hall Acoustics Calculator

Design a Schroeder QRD (Quadratic Residue Diffuser) panel by computing well depths, panel width, and effective diffusion bandwidth from design frequency and prime number.

Inputs

Design frequency (Hz)

Prime number (P)

Number of wells

Tab to move between fields

Results

Panel width (cm)

34.3

Individual well width (cm)4.9

Maximum well depth (cm)34.3

Lower diffusion limit (Hz)500

Upper diffusion limit (Hz)1,750

Unique well depths3

First well depth (cm)0

How to Use This Calculator

Enter Design frequency (Hz), Prime number (P), and Number of wells.
Review the Panel width (cm) result.
Use Individual well width (cm) and Maximum well depth (cm) to inform your decision.

How the result changes with Design frequency (Hz)

Design frequency (Hz)	Panel width (cm)
590	29.07
1,815	9.45
3,285	5.22
4,510	3.8

What each input means

Design frequency (Hz): The lowest frequency the diffuser is designed to scatter. Determines maximum well depth.
Prime number (P): Prime number for the QRD sequence (e.g. 5, 7, 11, 13, 17, 19, 23). Determines the number of wells per period.
Number of wells: Number of wells to compute depths for. Typically equals the prime number for one full period.

What each result means

Panel width (cm): Total width of one diffuser period (all wells combined) in centimeters.
Individual well width (cm): Width of each well in centimeters.
Maximum well depth (cm): Maximum possible well depth based on the design wavelength (half-wavelength).
Lower diffusion limit (Hz): Lower bound of the effective diffusion frequency range.
Upper diffusion limit (Hz): Upper bound of the effective diffusion frequency range.
Unique well depths: Number of distinct non-zero well depths in the QRD sequence.
First well depth (cm): Depth of the first well (well 0) in the quadratic residue sequence (always 0 cm).

How this is calculated

Worked example, using the default values

Identify Input Parameters
Design frequency (Hz) = 500, Prime number (P) = 7, Number of wells = 7 = 3 input(s) provided
Calculate Panel width
Panel width = wellWidth * primeNumber
34.3 = 34.3
Calculate Individual well width
Individual well width = (designWavelength / (2 * primeNumber)) * 100
4.9 = 4.9
Calculate Maximum well depth
Maximum well depth = (designWavelength / 2) * 100
34.3 = 34.3

Engine last updated July 28, 2026. Checked against 2 independently-derived tests — how we verify calculators.

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