Question

A theatre of volume $100 \times 40 \times 10m^3$ can accommodate 1000 visitors. The reverberation time of the theatre when empty is 8.5 s. If the theatre is now filled with 500 visitors, occupying the front-half seats, the reverberation time changes to 6.2 s. The average absorption coeficient of each visitor is nearly

• A. 0.6
• B. 0.5
• C. 0.45
• D. 0.7

Answer 1

Answer: (D)

Number of visitors = 1000
Volume of theatre = $100 \times 40 \times 10\, cm^3$
In first case
Volume acquired by one visitor $ = \frac{100 \times 40 \times 10}{1000} = 40\, m^3$
Reverberation time = 8.5 s
In second case
Volume acquired by one visitor $ = \frac{100 \times 40 \times 10}{500} = 80\, m^3$
Reverberation time = 6.2 s
The average absorbtion coefficent
$ \eta = \frac{40 \times 8.5}{80 \times 6.2} $
$ = \frac{85}{124} \approx 0.7 $