Question

An auditorium of dimensions $(100\times 40\times 10)m^3$ contains $1000m^2$ curtains of absorption coefficient $0.2m^{-2},2000m^2$ of carpets of absorption coefficient $0.7m^{-2}$. If $1000$ men of absorption coefficients $0.9$ per person are sitting in the hall, then reverberation time is

• A. $2.7s$
• B. $7.2s$
• C. $3.5s$
• D. $3.7s$

Answer 1

The correct option is A $2.7s$

Volume of the room $V=100\times 40\times 10=4\times {10}^4{m}^3$

Effective surface area of the room $A=\left(0.2\right)1000+\left(0.7\right)2000+\left(0.9\right)1000=2500$

Now reverberation time $T_r=0.161\frac{V}{A}$

$T_r=0.161\frac{4\times {10}^4}{2500}=2.576s$