The founding formula of architectural acoustics. Tie a hall's echo to two things only: how big the room is, and how much soft surface eats the sound. T60 = 0.161 · V / A — reverberation grows with volume and dies with absorption. Rendered, not quoted.
source Sabine, W. C., Architectural Acoustics: Reverberation, The American Architect & Building News (1900; derivation dated 29 Oct 1898) — reprinted in Collected Papers on Acoustics. Original serial has no stable single link — AMBER.
A room stores acoustic energy and leaks it through soft surfaces. Sabine found the decay is exponential: the sound level falls a fixed number of decibels per second. T60 is the time for a 60 dB drop — a fall to one-millionth of the energy.
Total absorption A = Σ Sₓ·αₓ in sabins: each surface's area times its absorption coefficient (α=0 mirror, α=1 open window). Then T60 = 0.161 V / A in SI. The constant 0.161 folds in the speed of sound and the geometry of a diffuse field.
This is the echo of a hall built on the-speed-of-sound. The 0.161 constant is literally 24·ln(10)/c at room temperature — Sabine's law inherits c ≈ 343 m/s from Newton and Laplace and folds it into a single measurable time.
Downstream: Helmholtz resonators, room modes, and reverberation engineering all sit on this founding 1898 result. Sabine turned a subjective "the hall sounds muddy" into an arithmetic anyone can compute before a brick is laid.
A live re-check of the engine's laws. It confirms V/A dependence, the doubling-halves law, and the anechoic limit — and flips RED the instant window 6 tampers the formula.
A rectangular hall. Set its volume and its total absorption; toggle a full audience, which adds soft bodies (more sabins).
Curve: sound level drops linearly in dB (exponential in energy). It reaches −60 dB exactly at T60 — that intercept is the engine's live output.
Proven result: a hall of V=10000 m³ with A=500 sabins rings for T60 = 3.22 s. Double the absorption → 1.61 s. Every number here is computed live from the law, not stored.
−S·ln(1−ᾱ) is the honest fix at high absorption.
It also ignores air absorption (matters above ~2 kHz in large halls), coupled rooms, and non-diffuse "flutter" between parallel walls. The single number T60 hides frequency dependence — a hall has a different reverberation at 125 Hz than at 4 kHz.
"A bigger hall always sounds worse / muddier."
→ Bigger raises T60, but concert halls want ~1.8–2.2 s. Too little reverberation (a dead studio) sounds worse for music.
"More absorption always improves a room."
→ Over-damping kills warmth. Absorption is a budget you tune, not maximise.
"The 0.161 constant is arbitrary / empirical fudge."
→ It is 24·ln(10)/c in SI — derived, and it changes with the speed of sound.
The disclosed planted void. Invert the law to T60 = 0.161·A/V. Now a bigger, less-absorptive hall would ring shorter — nonsense. The witness in window 7 catches it live.