---
title: "Mean free path in room (350 m/s)"
subject: "Engineering Physics"
chapter: 3
key: "semester_1/engineering_physics:room-mean-free-path-reflections-alt"
source: https://www.bctengineer.com/q/semester_1/engineering_physics/room-mean-free-path-reflections-alt
site: BCT Engineering
---

# Mean free path in room (350 m/s)

Engineering Physics · Chapter 3: Acoustics

- Asked in: 2068 Chaitra, 5 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_1/engineering_physics/room-mean-free-path-reflections-alt
- Whole chapter: https://www.bctengineer.com/md/semester_1/engineering_physics/chapter-3

## Question

A room has dimensions 6m×4m×5m. Find: i) Mean free path of sound wave in the room ii) The number of reflections made per second by the sound wave with the walls of the room. (Take velocity of sound in air = 350 ms⁻¹)

## Short answer

Mean free path d = 4V/S = 4×120/148 = 3.24 m. Reflections per second n = v/d = 350/3.24 ≈ 108.

## Answer

The **mean free path** of sound is the average distance travelled between two successive reflections: *d* = 4V/S. The number of reflections per second is *n* = v/d.

**Given:** room 6 m × 4 m × 5 m, v = 350 m/s.

#### i) Mean free path
1. V = 6 × 4 × 5 = 120 m³
2. S = 2(6×4 + 4×5 + 6×5) = 2(24 + 20 + 30) = 148 m²
3. d = 4V/S = 480/148 = **3.24 m**

#### ii) Reflections per second
n = v/d = 350 / 3.243 = 107.9

**Answer: (i) 3.24 m; (ii) about 108 reflections per second.**

## Check yourself

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

1. For a 6 × 4 × 5 m room (V = 120 m³, S = 148 m²), the mean free path 4V/S is
   A. 3.24 m
   B. 0.81 m
   C. 6.48 m
   D. 1.62 m
   Answer: A. 4 × 120/148 = 3.24 m. (Key point: Mean free path)

2. The number of reflections per second is found from
   A. n = d/v
   B. n = v/d
   C. n = v d
   D. n = V/S
   Answer: B. Sound travels v metres per second and covers d metres per reflection, so n = v/d. (Key point: Reflection rate formula)

3. With v = 350 m/s, the reflections per second are about
   A. 10.8
   B. 1080
   C. 92.6
   D. 108
   Answer: D. n = 350/3.243 ≈ 108. (Key point: Result)

## Close variants set in other exams

- [Mean free path and reflections in room](https://www.bctengineer.com/question.md?key=semester_1%2Fengineering_physics%3Aroom-mean-free-path-reflections) — Engineering Physics, chapter 3, asked 2×