Sound Diffuser Calculator

QRD Well Depth Formula:

\[ d_k = \frac{(k^2 \mod N) \times \lambda_{\text{min}}}{2N} \]

Well Depth (d_k):

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1. What is a Quadratic Residue Diffuser?

A Quadratic Residue Diffuser (QRD) is an acoustic diffuser designed using number theory principles to scatter sound waves evenly across a space. It consists of wells of different depths calculated using quadratic residue sequences.

2. How Does the Calculator Work?

The calculator uses the QRD well depth formula:

\[ d_k = \frac{(k^2 \mod N) \times \lambda_{\text{min}}}{2N} \]

Where:

\( d_k \) — Depth of the k-th well (meters)
\( k \) — Well index (0, 1, 2, ..., N-1)
\( N \) — Design number (prime number)
\( \lambda_{\text{min}} \) — Minimum wavelength to diffuse (meters)
\( \mod \) — Modulo operation

Explanation: The formula calculates the optimal depth for each well in a QRD based on quadratic residue sequences, which creates an effective acoustic diffuser.

3. Importance of Well Depth Calculation

Details: Accurate well depth calculation is crucial for creating effective acoustic diffusers that properly scatter sound waves, reduce standing waves, and improve acoustic quality in rooms.

4. Using the Calculator

Tips: Enter the well index (k), design number (N, typically a prime number), and the minimum wavelength to diffuse. All values must be valid positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the optimal design number N for QRD?
A: N should be a prime number (typically 7, 11, 13, 17, etc.) to ensure proper diffusion characteristics.

Q2: How do I determine the minimum wavelength?
A: The minimum wavelength is determined by the highest frequency you want to diffuse: λ_min = speed of sound / frequency_max.

Q3: What materials are best for constructing QRD diffusers?
A: Common materials include wood, acrylic, or MDF. The material should be rigid and non-porous to properly reflect sound waves.

Q4: How many wells should a QRD have?
A: The number of wells equals the design number N. More wells provide better diffusion but require more space.

Q5: Where should QRD diffusers be placed in a room?
A: Typically on rear walls, side walls at reflection points, or on ceilings to break up standing waves and flutter echoes.