Sabina

Sabina lifts her baton and the echo rings fade on schedule, right when she says they will.

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.

T₆₀ = 0.161 V / A, A = Σ S α

• T₆₀: time for sound to fall by 60 dB (s)
• V: room volume (m³)
• A: total absorption (m²)
• S: area of each surface (m²)
• α: absorption coefficient of that surface

Wallace Clement Sabine, Harvard, late 1890s; Boston Symphony Hall, 1900.

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.

On the shirt

Front: Sabina, the pixel-art character, with “THE ECHO HAS A CLOCK”. Back: Sabine's law, the absorption sum, the 60 dB definition and the Symphony Hall figure. Printed on a unisex tee.