Good acoustic building, reverberation time

Good acoustics means every listener hears the sound clearly, with enough loudness and without echo, distortion or noise. Reverberation is the persistence of sound in a hall after the source stops, due to repeated reflections.

Measures for good acoustics

1. Reverberation time should be optimum (about 0.5-1 s for speech rooms, 1.5-2 s for music halls).
2. Loudness: use a low ceiling or a sloping, curved reflecting sounding board behind the speaker so that sound reaches the back seats.
3. Absorbing materials: line walls and ceiling with felt, acoustic tiles, heavy curtains, carpets, perforated boards. Audience and cushioned seats also absorb.
4. No echoes: avoid large flat parallel walls and concave surfaces that focus sound; use irregular surfaces and diffusers.
5. Sound distribution: keep the sound uniform in all parts using properly placed loudspeakers.
6. Noise control: use double doors/windows, and keep the hall away from traffic and machinery.
7. Resonance: avoid wooden panels or hollow boxes that resonate with particular frequencies.

Reverberation time and absorption (Sabine's formula)

Let V = volume of hall, S₁, S₂ ... surface areas with absorption coefficients a₁, a₂ ..., A = ΣaS (total absorption), E = sound energy density, c = speed of sound.

1. Sound energy falling per second on the surfaces is (cE/4) per unit area, so the energy absorbed per second = (cE/4)·A.
2. This equals the loss of total energy: V dE/dt = −(c A/4) E.
3. Integrating: E = E₀ e^(−cAt/4V).
4. Reverberation time T is the time for the energy to fall to 10⁻⁶ of the initial value: 10⁻⁶ = e^(−cAT/4V).
5. Taking logs: ln(10⁶) = 13.8 = cAT/(4V), so T = 55.3 V/(cA).
6. With c = 343 m/s:

T = 0.161 V / ΣaS      (V in m³, S in m², T in s)

Since V is fixed for a given hall, T ∝ 1/A. When the absorbing factor (a or area S of absorbers) increases, ΣaS increases and the reverberation time decreases. Hence adding carpets, curtains and audience reduces reverberation.