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Mean free path in room (350 m/s)

Short answer

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

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)

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.

✓ Answer checked by Claude Opus 5.5 (high effort)

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