Reverberation Time⚠ unverified
Physics / Acoustics · Compute the Sabine reverberation time (T60)
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| V | V | m**3 | 1.0 | Room volume |
| A | A | m**2 | 1.0 | Total absorption of the room |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | T60 | s | Reverberation time, in seconds (s). Returns positive infinity when ``A`` is not positive |
The science & history
Understanding the Parameters
- $V$ — larger rooms ring longer at fixed absorption.
- $A$ — equivalent absorbing area; $\alpha$ is the random-incidence absorption coefficient.
- $T_{60}$ — speech rooms often target ~0.5–1 s; halls longer. Eyring’s formula is better when average $\alpha$ is high.
Derivation (Approaching a Proof)
Energy density decays as the mean free path and wall absorption remove energy each collision. Sabine’s statistical model yields $T_{60} \propto V/A$. The constant 0.161 s/m in SI comes from $24\ln(10)/c$ with $c \approx 343$ m/s (order-of-magnitude: $55.3/c$).
History
Wallace Clement Sabine founded architectural acoustics with RT measurements at Harvard (c. 1895); $T_{60}$ remains the primary room-acoustic metric.
Related Concepts: Sound Pressure Level, Sound Attenuation, Insertion Loss
Notes: Registry calculator reverberation-time (unverified). Sabine formula; diffuse-field
assumption.