Question

The reverberation time of a room is t seconds. Another room of double the dimensions with the walls of the same absorption coefficient will have a reverberation time :

• A. $t^2$
• B. $2t$
• C. $t/2$
• D. t${}^3$

Answer 1

The correct option is B $2t$

Given: $\frac{V_1}{V_2}=\frac{1}{8}\frac{A_1}{A_2}=\frac{1}{4}$
$R.T{.}_1=t$
$R.T=0.161\frac{v}{A}$
$\frac{R.T{.}_1}{R.T{.}_2}=\frac{0.161\times \frac{v_1}{A_1}}{0.161\times \frac{v_2}{A_2}}=\frac{v_1{A}_2}{v_2{A}_1}=\frac{1}{8}\times \frac{4}{1}=\frac{1}{2}$
$R.T_2=2R.T_1$
$=2\times t$
$=2t$