Scattering Coefficients Explained
Education · 10 min read · ResonAia Editorial
Demystify acoustic scattering coefficients. Learn how diffuser performance is measured, what the numbers mean, and how to interpret specifications.
What is a Scattering Coefficient?
The scattering coefficient (s) quantifies how much of the reflected sound energy is scattered versus specularly reflected. It ranges from 0 to 1:
- s = 0: Perfect mirror. All energy reflects at the specular angle (like a flat wall)
- s = 1: Perfect diffuser. Energy scattered uniformly across all angles
- s = 0.7: 70% of energy scattered, 30% specularly reflected
Real diffusers fall somewhere between these extremes, with good diffusers achieving s > 0.7 at design frequencies.
Measurement Standards
ISO 17497-1
ISO 17497-1 describes measurement of the random-incidence scattering coefficient in a reverberation-room context.
ISO 17497-2
ISO 17497-2 describes measurement of the directional diffusion coefficient in a free-field context.
Both are useful for diffuser evaluation, but they answer different questions: how much energy leaves the specular direction versus how uniformly energy is distributed by angle. Manufacturer data sheets should specify which standard — and which coefficient — is being reported, since the two aren't directly interchangeable.
Frequency Dependence
Scattering coefficients vary dramatically with frequency. A well-designed diffuser might show:
| Frequency | Scattering Coefficient |
|---|
| 125 Hz | 0.1 |
| 250 Hz | 0.3 |
| 500 Hz | 0.7 |
| 1000 Hz | 0.9 |
| 2000 Hz | 0.85 |
| 4000 Hz | 0.7 |
Low-Frequency Limit
Below a cutoff frequency, diffusers become acoustically transparent. The wavelength is too long to interact with the surface structure. Frequency limits here are planning estimates, not precise cutoffs — the low limit is mainly constrained by maximum well depth.
Approximate rule: f_low ≈ c / (4 × d_max)
For a diffuser with 15cm maximum depth: f_low ≈ 343 / (4 × 0.15) ≈ 572 Hz
Below roughly 500-600 Hz, this diffuser provides minimal scattering, as a planning estimate. Exact performance depends on the diffuser family, panel size, incidence angle, arraying, and measurement method.
High-Frequency Limit
Above a certain frequency, the wells become too wide relative to wavelength, and scattering degrades. The high limit is mainly constrained by well/element width and edge detail:
f_high ≈ c / (2 × w)
For 5cm well width: f_high ≈ 343 / (2 × 0.05) ≈ 3430 Hz
Scattering is most effective between these limits, typically a 2-3 octave range — again, treat this as a planning estimate rather than a precise boundary.
Interpreting Manufacturer Data
What to Look For
Frequency-specific values: Good manufacturers provide coefficients at standard octave bands. Beware single-number claims.
Test standard reference: Should cite ISO 17497 or equivalent.
Panel size tested: Larger panels perform better in tests. A 60cm panel tested in a 4m² array represents real-world better than isolated small-panel tests.
Mounting conditions: Were panels tested with air gap? Against hard backing? This affects results.
Red Flags
Single number for all frequencies: Physically impossible. Scattering always varies with frequency.
Claims of s = 0.95+ across full range: Even the best diffusers show frequency variation.
No test standard cited: Likely untested marketing claims.
Claims for thin products: Using the depth-based estimate above, a 2" deep product is unlikely to meaningfully scatter frequencies much below ~1700 Hz. Treat any marketing claim of strong low-frequency performance from a thin panel with skepticism.
Scattering vs Diffusion Coefficient
These terms are sometimes used interchangeably but technically differ:
Scattering Coefficient (s)
- Measures how much energy leaves the specular direction
- Doesn't care WHERE the energy goes
- A curved surface has high scattering but non-uniform polar pattern
Diffusion Coefficient (d)
- Measures how UNIFORMLY energy is scattered
- Normalized to a theoretical perfect diffuser
- Prefers energy spread evenly across all angles
A perfect diffuser has both s = 1 and d = 1. Real diffusers optimize for high values of both.
Why It Matters
Some surfaces scatter sound (s = high) but don't diffuse it well (d = low). A curved wall scatters but focuses energy at certain angles. A QRD both scatters AND diffuses, spreading energy uniformly.
For acoustic treatment, you generally want both high scattering AND high diffusion.
Practical Application
Comparing Products
When evaluating diffusers:
- Check performance at your frequencies of interest
- For voice/music: look at 500-4000 Hz data
- For low-frequency extension: check 250-500 Hz performance
- Compare depth to expected low-frequency limit
Estimating Performance from Design
Our diffuser designer predicts scattering coefficients based on well geometry. While lab measurement is most accurate, computational predictions correlate well for standard designs.
Deeper wells = better low-frequency scattering Narrower wells = better high-frequency scattering More wells (larger N) = more uniform diffusion
Multiple Reflections
In real rooms, sound reflects multiple times. Cumulative effect of moderate scattering (s = 0.5) over several reflections approaches the effect of high scattering on first reflection.
Don't over-specify: s = 0.6-0.7 diffusers often provide adequate treatment.
Measurement DIY
You can't measure ISO 17497 without specialized equipment, but qualitative tests help:
Clap test: Face the diffuser 2m away. Clap and listen. You should hear diffuse decay rather than discrete echo.
Comparison test: Same clap test against flat wall at same distance. Diffuser should sound distinctly different, less sharp, more spread.
Balloon pop: Pop balloon 1m from diffuser. Record the impulse. Compare waveform to reflection from flat surface.
These don't give you numbers but verify that your diffuser is actually scattering sound.
Scattering, Diffusion, Acoustics, Measurement
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