Reverberation time is defined as the time during which the intensity of sound in the auditorium becomes one millionth of the initial intensity.

Sabine has shown that standard reverberation time for an auditorium is given by the formula

${T_R} = K{V \over {\alpha S}}$

Here, V is volume of the auditorium, S is the surface area.

$\therefore {T_R} = {{K.V} \over {\alpha S}} = 1$ (given)

$\Rightarrow {T_R} = {{K.{l^3}} \over {6\alpha {l^2}}} = {K \over {6\alpha }}l$ ${T_R} = {{K.{l^3}} \over {6\alpha {l^2}}} = {K \over {6\alpha }}l$
(Assuming auditorium to be cubic in shape)

$\therefore {T_R} \propto l$

If dimension is doubled, reverberation time t will be doubled.
So, New T_R = 2 sec.