Question

The ratio of the absorption of a person to that of an auditorium is 1/1200. In order to make the reverberation time 3/4th of the initial value, the number of persons to be accommodated in the auditorium are

• A. 200
• B. 400
• C. 100
• D. 700

Answer 1

Answer: (B)

400

The reverberation time of the auditorium with volume V and total absorption coefficient A is given by:

$T_1=\frac{0.17V}{A}$

Now when we will include n number of people each having a absorption coefficient $A_p$ in the auditorium then the reverberation time of the auditorium will be:

$T_2=\frac{0.17V}{A+n{A}_p}$.

According to question: $\frac{T_2}{T_1}=\frac{3}{4}$

Substituting the above formula for $T_1$ and $T_2$ we will get $n=400$.