Eyring Equation
Definition
Eyring Equation
The Eyring equation, developed by Carl Eyring in 1930, predicts reverberation time more accurately than the Sabine equation for rooms with high average absorption coefficients. It uses the natural logarithm of the survival coefficient (1 - mean absorption) to account for the multiplicative nature of sound energy loss at each surface reflection. SonaVyx computes both Sabine and Eyring predictions.
T60 = 0.161 × V / (-S × ln(1 - ā)), where ā = weighted mean absorption coefficient, S = total surface area
How It Is Measured
Like the Sabine equation, the Eyring equation is a predictive tool rather than a measurement. SonaVyx calculates both Sabine and Eyring RT60 predictions and compares them to measured values. The weighted mean absorption coefficient is computed by dividing total absorption by total surface area. When ā approaches zero, the Eyring equation converges to the Sabine result.
Practical Example
A recording studio vocal booth (2.5 × 2 × 2.4 m, V = 12 m³, S = 28.8 m²) is heavily treated with acoustic foam (mean α = 0.55). Sabine predicts T60 = 0.161 × 12 / (28.8 × 0.55) = 0.12s. Eyring predicts T60 = 0.161 × 12 / (-28.8 × ln(0.45)) = 0.084s. The Eyring prediction is 30% lower and more accurate for this highly absorptive space.
Why Eyring Is More Accurate
The Sabine equation assumes each sound ray has a probability α of being absorbed at each reflection. The Eyring equation correctly models that a sound ray surviving N reflections retains (1-ā)ᴺ of its original energy. This exponential decay is more physically accurate, especially when ā is large. When ā is small, (1-ā) ≈ e^(-ā), and both equations give the same result. The divergence becomes significant above ā = 0.20.
Fitzroy Equation
The Fitzroy equation extends Eyring for rooms with highly non-uniform absorption — for example, one wall with heavy treatment and three bare walls. It computes separate decay rates for each pair of opposing surfaces and takes the harmonic mean. SonaVyx computes Fitzroy RT60 when room surface data is entered, providing three predictions (Sabine, Eyring, Fitzroy) for the most complete analysis.
Practical Differences
For a typical untreated office (ā ≈ 0.10), Sabine and Eyring differ by less than 5%. For a moderately treated room (ā ≈ 0.30), the difference reaches 15%. For a heavily treated studio (ā ≈ 0.60), the difference exceeds 30%. In extreme cases (ā approaching 1.0), Sabine predicts a finite RT60 while Eyring correctly approaches zero — a room with perfect absorption should have no reverberation.
Try It Now
Compare Sabine vs Eyring predictions — free RT60 calculator