廣泛使用

QRD 擴散器設計二次餘數擴散器

QRD 擴散器是應用最廣泛、研究最透徹的聲學擴散器類型。基於 Manfred Schroeder 在 1970 年代的開創性工作，QRD 擴散器使用數學推導的槽深，在寬頻率範圍內可預測地散射聲音。

What is a QRD Diffuser?

Mathematical Foundation

QRD (Quadratic Residue Diffuser) is a reflection phase-grating diffuser invented by Dr. Manfred Schroeder in the 1970s. It uses number theory to create a sequence of well depths that scatter sound evenly across a wide range of frequencies.

The quadratic residue sequence ensures that reflected sound waves arrive at different phases, preventing destructive interference and creating smooth, even diffusion.

How It Works

Each well in a QRD diffuser has a depth determined by the formula rk = k² mod N, where N is a prime number. The prime number N determines how many wells the diffuser has and affects its frequency range.

Common prime numbers used are 7, 11, 13, 17, and 23. Larger primes create more wells and provide diffusion over a wider frequency range, but require more complex fabrication.

Acoustic Properties

QRD diffusers scatter sound in a hemisphere pattern (for 1D QRDs, it's a semicircle). They maintain the energy of reflections while eliminating specular (mirror-like) reflections that can cause flutter echoes and comb filtering. Diffusion does not eliminate low-frequency standing waves — those still require bass trapping, source/listener repositioning, or room-geometry changes.

The design frequency (lowest frequency effectively diffused) is a planning estimate determined mainly by the maximum well depth: fmin = c / (4 × depth), where c is the speed of sound (~343 m/s). Exact performance depends on panel size, incidence angle, and arraying, and should be confirmed by simulation or measurement.

使用情境

Recording Studio Control Rooms. Ideal for the rear wall of control rooms to eliminate early reflections while maintaining room liveliness. Creates an accurate stereo image and reduces fatigue during long mixing sessions.
Live Rooms & Tracking Spaces. Provides natural-sounding diffusion for drum rooms, vocal booths, and live recording spaces. Preserves the energy of the room while controlling problematic reflections.
Home Theaters & Listening Rooms. Enhances the spaciousness of home theaters without adding excessive reverberation. Particularly effective on sidewalls and rear walls to widen the soundstage.
Broadcast & Post-Production. Creates controlled acoustics for voice recording, ADR stages, and post-production rooms. Reduces flutter echo and specular reflections while maintaining speech intelligibility.
Auditoria & Performance Spaces. Large-scale QRD diffusers can be used on sidewalls and rear walls of concert halls to provide uniform sound distribution and prevent echoes.
Flutter Echo Treatment. Excellent for eliminating flutter echoes between parallel walls without over-damping the space. Works well in combination with absorption for balanced acoustics.

優點

Well-established and extensively researched design
Predictable and consistent acoustic performance
Relatively simple to manufacture with CNC equipment
Works well across a broad frequency range (typically 500Hz-4kHz)
Symmetric pattern creates balanced diffusion
Can be designed for specific frequency ranges
Widely used in studio and architectural acoustic practice
Multiple design options by varying the prime number N

注意事項

One-dimensional diffusion only (use 2D QRD for hemispherical)
Limited effectiveness at very low frequencies (below ~400Hz)
Requires significant panel depth for low-frequency diffusion
Can be expensive to fabricate compared to simple absorbers
Visual appearance may not suit all architectural styles
Fixed design - not adjustable after construction
Requires precise fabrication for optimal performance
May accumulate dust in deep wells (maintenance consideration)

設計參數

Prime Number (N). Common values: 7, 11, 13, 17, 23: The prime number determines the number of wells in the diffuser. Larger primes provide broader frequency coverage but increase manufacturing complexity.
Maximum Well Depth. Typical range: 50mm - 200mm (2" - 8"): Determines the lowest frequency that will be effectively diffused, as a planning estimate. Calculated as: depth = λ/4 = c/(4×fmin)
Well Width. Typical range: 20mm - 100mm (0.8" - 4"): Affects the highest frequency that will be diffused. Narrower wells extend the upper frequency limit, as a planning estimate. Must be less than half the wavelength at the design frequency.
Panel Width. Typical range: 600mm - 1200mm (24" - 48"): The total width of one complete diffuser panel. Multiple panels are typically used to cover larger wall areas. Should be at least 3× the design wavelength.
Frequency Range. Planning range: Typically 400Hz - 4kHz: Frequency limits are planning estimates. The low limit is mainly constrained by maximum well depth; the high limit is mainly constrained by well width and edge detail. Exact performance depends on panel size, incidence angle, arraying, and measurement method.
Material Selection. Common materials: MDF, plywood, hardwood: Material should be rigid and non-porous. MDF is popular for CNC fabrication due to consistent density and smooth finish. Wood species affect aesthetics and cost.

How to Design a QRD Diffuser

Choose your goal and placement. Decide where the diffuser will go (rear wall, ceiling, etc.) and what problem you are solving (flutter echo, spaciousness, rear-wall reflections).
Select a sequence length (N). Pick a prime number N, which determines the number of wells and influences the overall width and pattern repetition.
Choose maximum well depth. Set the maximum well depth based on your desired lowest effective frequency (often approximated with quarter-wavelength depth).
Set well width and panel size. Choose well width and overall panel dimensions that fit your space and fabrication method.
Build and install. Use rigid materials, keep tolerances consistent, and install at the planned location with adequate distance from the listening position.

擴散器設計器 · 價格

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