---
title: "Good acoustic building, reverberation time"
subject: "Engineering Physics"
chapter: 3
key: "semester_1/engineering_physics:acoustic-measures-reverberation-decrease"
source: https://www.bctengineer.com/q/semester_1/engineering_physics/acoustic-measures-reverberation-decrease
site: BCT Engineering
---

# Good acoustic building, reverberation time

Engineering Physics · Chapter 3: Acoustics

- Asked in: 2073 Shrawan, 5 marks
- Video: [Acoustics of Buildings](https://www.youtube.com/watch?v=TkadZL-sTU8) — Self Learn
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_1/engineering_physics/acoustic-measures-reverberation-decrease
- Whole chapter: https://www.bctengineer.com/md/semester_1/engineering_physics/chapter-3

## Question

What are the measures of good acoustic building? Show that the reverberation time decreases with increase in absorbing factors in a hall.

## Short answer

Good acoustics requires optimum reverberation time, absorbent surfaces (carpets, curtains, acoustic tiles), proper loudness via reflectors, no echoes, uniform sound distribution, and noise isolation. Sabine’s formula T = 0.161V/ΣaS shows T ∝ 1/ΣaS; increasing total absorption by adding absorbents decreases reverbration time.

## Answer

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, *S*₁, *S*₂ ... surface areas with absorption coefficients *a*₁, *a*₂ ..., *A* = Σ*aS* (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:

```text
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.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. Which is a recommended measure for good hall acoustics?
   A. Large flat parallel walls
   B. Concave surfaces to focus sound
   C. Absorbing materials like curtains, carpets and acoustic tiles
   D. Hollow wooden boxes that resonate
   Answer: C. Absorbers control reverberation, whereas flat parallel walls, concave surfaces and resonating panels cause echoes or focusing. (Key point: Measures for good acoustics)

2. For a hall of fixed volume, Sabine's formula shows reverberation time T is
   A. proportional to ΣaS
   B. independent of ΣaS
   C. proportional to 1/ΣaS
   D. proportional to (ΣaS)²
   Answer: C. T = 0.161V/ΣaS, so T ∝ 1/A when V is fixed. (Key point: Proportionality of T)

3. What happens to reverberation time when carpets, curtains and audience are added?
   A. It increases
   B. It decreases
   C. It stays the same
   D. It becomes infinite
   Answer: B. More absorption raises ΣaS in the denominator, lowering T. (Key point: Effect of adding absorbers)

4. Which equation leads to E = E0 e^(-cAt/4V)?
   A. V dE/dt = -(cA/4)E
   B. V dE/dt = (cA/4)E
   C. dE/dt = -cAV
   D. E = cA/4V
   Answer: A. Energy loss rate equals energy absorbed per second, (cE/4)A, and integrating gives the exponential. (Key point: Energy decay step)

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