Quadratic Residue Diffusers (QRD)

The quadratic residue diffuser , often also called a Schroeder diffuser , belongs to the group of pseudostochastic diffusers. Its purpose is to scatter incoming sound waves in a controlled manner in order to avoid flutter echoes and create a lively yet controlled sound image in the room.

Structure and Function

A QRD consists of a series of parallel chambers (strips) of varying depths. These chambers are precisely isolated from one another by thin partitions. For optimal effectiveness, the entire structure must be made of acoustically reflective material such as wood, metal, or stone.

One-dimensional QRDs: These scatter the sound primarily in a plane that is perpendicular to the course of the individual stripes.

Two-dimensional QRDs: These consist of an arrangement of individual fields (e.g. 49 fields for the prime number 7) and scatter sound arriving from any direction.

The mathematical basis

The depth ratios of a QRD are based on a quadratic residue sequence , which is calculated using a prime number. This prime number defines the period length and the number of stripes. In practice, the prime numbers 7, 11, or 13 are most commonly used.

The deeper the shafts are dimensioned, the lower the cutoff frequency at which the sound is still diffusely reflected.

Planning the building depth

The wavelength is crucial for acoustic effectiveness:

A depth of approximately half the wavelength ( λ/2 ) of the desired lower cutoff frequency is required.
The more strips (higher prime number) are used, the larger the effective frequency range of the diffuser becomes.

Alternative: Primitive Root Diffusers (PRD)

Related to the QRD are primitive root diffusers . They utilize a primitive root sequence for fringe depths. Their distinctive feature is uniform diffuse scattering combined with reduced reflection in the direct geometric mirror direction.