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GATE 2021 AR – Question 54

Building Services · Acoustics in buildings · 2 marks · Numerical answer

A hall measures 8×14×4 m and has four 1.5×1.0 m windows and two 1×2 m doors. Wall, floor and ceiling absorption coefficient is 0.2; closed doors/windows 0.4. With windows open and doors closed, find reverberation time in seconds, to two decimals.

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Correct answer: 0.82 to 0.86

Explanation

Volume is 448 m³ and total enclosing surface is 400 m². Open windows occupy 6 m², closed doors 4 m², leaving 390 m² ordinary surface. Equivalent absorption is 390×0.2+6×1+4×0.4=85.6 m² sabin. Sabine’s T=0.161×448/85.6≈0.843 s, or 0.84 s. An open window uses absorption near 1 rather than the closed-window coefficient.

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