Sabine Equation
Definition
Sabine Equation
The Sabine equation, formulated by Wallace Clement Sabine in 1898, predicts the reverberation time of a room from its volume and total absorption area. It assumes perfectly diffuse sound field and uniform absorption distribution. SonaVyx uses the Sabine equation in its treatment calculator to predict RT60 changes when absorption is added to a room.
T60 = 0.161 × V / A (seconds), where V = room volume (m³), A = total absorption (m² Sabins)
How It Is Measured
The Sabine equation is not directly measured but is used to predict RT60 from known room dimensions and material absorption coefficients. SonaVyx compares the Sabine prediction against measured RT60 to validate room acoustic models. If measured and predicted values differ significantly, the room may have non-uniform absorption, focusing effects, or flutter echo paths not accounted for in the diffuse-field assumption.
Practical Example
A rectangular meeting room measures 8 × 6 × 3 meters (volume = 144 m³). The walls are painted plaster (α = 0.05), ceiling is acoustic tile (α = 0.70), and floor is carpet (α = 0.30). Total absorption A = walls(84×0.05) + ceiling(48×0.70) + floor(48×0.30) = 4.2 + 33.6 + 14.4 = 52.2 m². Sabine RT60 = 0.161 × 144 / 52.2 = 0.44 seconds — well within the speech target range.
Derivation and Assumptions
Sabine derived his equation empirically by measuring reverberation times in Harvard lecture halls with varying amounts of seat cushions. The equation assumes a perfectly diffuse sound field where sound energy is distributed uniformly throughout the room and strikes all surfaces equally. This assumption is reasonable for rooms with moderate, evenly distributed absorption but breaks down in very absorptive or irregularly shaped spaces.
Total Absorption (A)
Total absorption A is the sum of each surface area multiplied by its absorption coefficient: A = Σ(Sᵢ × αᵢ). Absorption coefficients range from 0.01 (polished marble) to 0.99 (deep wedge anechoic foam). Occupied seats contribute additional absorption — each person adds approximately 0.5 m² Sabins. SonaVyx maintains a database of 55 materials with per-octave-band absorption coefficients for accurate predictions.
When Sabine Fails
The Sabine equation overestimates RT60 when average absorption exceeds approximately 0.20, because the diffuse-field assumption breaks down with highly absorptive surfaces. In these cases, the Eyring equation provides more accurate predictions. For rooms with very non-uniform absorption (e.g., one highly absorptive wall and three reflective walls), the Fitzroy equation accounts for the directional variation in decay rates.
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