Sabina: Echo Has a Clock
Optics, Waves & Sound arc, page 115 of 193. Back to The Pixelated Physics Universe
Who they are
Sabina lifts her baton and the echo rings fade on schedule, right when she says they will.
Sabina is a character of the Optics, Waves & Sound arc: drawn in pixels, ruled by one piece of real physics, and never allowed to break it.
The physics
In the late 1890s Wallace Sabine, a young Harvard physicist, was asked to fix a lecture room where speech lingered for seconds. Timing how long a sound stayed audible as he brought in seat cushions, he found that reverberation time is proportional to the room's volume divided by its total absorption. The 0.161 comes from 24 ln 10 / c with c ≈ 343 m/s. He went on to advise on Boston's Symphony Hall, which opened in 1900 and is often described as the first concert hall whose acoustics were designed with a quantitative formula. Its occupied reverberation time is about 1.9 s.
$$ \begin{gathered} T_{60} = \frac{0.161\,V}{A} \\ A = \sum_i S_i\,\alpha_i \end{gathered} $$
| Symbol | Meaning | SI unit |
|---|---|---|
| $T_{60}$ | reverberation time: time for sound to fall by 60 dB | s |
| $0.161$ | constant 24 ln 10 / c for c = 343 m/s | s/m |
| $V$ | room volume | m³ |
| $A$ | total absorption | m² |
| $S_i$ | area of surface i | m² |
| $\alpha_i$ | absorption coefficient of surface i | 1 |
Honest caveat: Sabine's formula is not exact: it fails for very absorbent rooms, where Eyring's version does better. Sabine's own calculation for Symphony Hall gave 2.31 s, as reported in E. Thompson's history The Soundscape of Modernity (2002); historians attribute the overestimate to how he counted audience absorption.
Sources
- Sabine (1906) Architectural Acoustics, Proc. Am. Acad. Arts Sci. 42, 51
- Boston Symphony Orchestra, History of Symphony Hall
Crossovers
Sabina meets Murmura (Whispering Gallery). Sabina's echo dies at a rate set by the room's absorption: her reverberation time. Murmura keeps a whisper alive by skimming it along the wall. One room is designed to quiet sound, the other carries it.
Sabina meets Levitah (Held by Sound). Sabina's echo returns after the sound travels to a wall and back, about 343 m/s at room temperature. Levitah uses reflected sound too: an emitter and a reflector set up a standing wave whose pressure nodes can hold a small bead in air.
Wear the lore
Concept keywords: Echo Has a Clock, Sabina, Optics, Waves & Sound, physics lore, Pixelated Physics