---
title: "Average absorption coefficient of a hall"
subject: "Engineering Physics"
chapter: 3
key: "semester_1/engineering_physics:reverberation-absorption-coefficient-hall"
source: https://www.bctengineer.com/q/semester_1/engineering_physics/reverberation-absorption-coefficient-hall
site: BCT Engineering
---

# Average absorption coefficient of a hall

Engineering Physics · Chapter 3: Acoustics

- Asked in: 2074 Chaitra, 5 marks
- Video: [8. Absorption Coefficient and its Measurements | Acoustics](https://www.youtube.com/watch?v=jZTMLUqsOyI) — MKS TUTORIALS by Manoj Sir
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_1/engineering_physics/reverberation-absorption-coefficient-hall
- Whole chapter: https://www.bctengineer.com/md/semester_1/engineering_physics/chapter-3

## Question

A reverberation time of 2.3 sec is observed in a hall of volume 5500 m³. The sound absorbing surface of the hall has an area of 750 m². Calculate the average absorption coefficient.

## Short answer

Using Sabine’s formula T = 0.161V/(āS), the average absorption coefficient is ā = 0.161V/(TS) = (0.161×5500)/(2.3×750) ≈ 0.51.

## Answer

Given: reverberation time T = 2.3 s, volume V = 5500 m³, sound-absorbing surface area S = 750 m².

**Formula (Sabine):**
```text
T = 0.161 V / (ā S)     →     ā = 0.161 V / (T S)
```
(V in m³, S in m², T in s; 0.161 s/m is 4 ln(10⁶)/c with c = 343 m/s.)

#### Steps
1. Numerator: 0.161 × 5500 = 885.5 s·m².
2. Denominator: T × S = 2.3 × 750 = 1725 s·m².
3. ā = 885.5 / 1725 = 0.513.

(Equivalently, the total absorption is A = ā S = 0.161 V/T = 385 m² of open window, i.e. 385 sabins.)

**Answer: the average absorption coefficient is ā ≈ 0.51 (dimensionless; about 51% of the incident sound is absorbed).**

## Check yourself

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

1. To find the average absorption coefficient from T = 0.161V/(āS), we use
   A. ā = T S / (0.161 V)
   B. ā = 0.161 V T / S
   C. ā = 0.161 V / (T S)
   D. ā = 0.161 S / (T V)
   Answer: C. Solving for ā gives 0.161V divided by T times S. (Key point: Rearranging Sabine formula)

2. The average absorption coefficient is about
   A. 0.051
   B. 1.95
   C. 0.51
   D. 5.1
   Answer: C. ā = 885.5/(2.3 × 750) = 885.5/1725 ≈ 0.513. (Key point: Result)

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