$V=\sqrt{\frac{\gamma R T}{M}}$

Volume before expansion $=V_{b}$

Volume after expansion $=V_{a}$

Temp before expansion $=T_{b}$

Temp after expansion $=T_{a}$.

As, Volume os Temperature,

$\frac{V_{b}}{V_{a}}=\frac{T_{b}}{T_{a}}=\frac{V_{b}}{2 V_{b}}=\frac{1}{2}$

$\therefore \frac{T_{b}}{T_{a}}=\frac{1}{2}$

Whow, Before expansion,

$C_{b}=\sqrt{\frac{\gamma R T_{b}}{I M}}$ $\dots \; (1)$

After exparsion,

$C_{a}=\sqrt{\frac{\gamma R T_{a}}{M}}$ $\dots \; (2)$

eq.  $1/2$

$\frac{c_{b}}{c_{a}}=\sqrt{1 / 2} \quad \therefore \quad c_{a}=\sqrt{2} c_{b}$.