Answer
$c_{1}/c_{2} = 1.41$
Work Step by Step
Given that temparature $T1= 350.2K$
Initial air pressure $P_{1} =2.2$
Final air pressure $P_{2} = 0.4$
Specific heat ratio $k = 1.667$
As per the relation between P and T
$p_{1}/p_{2} = (T_{1}1/T_{2})^(k/(k-1))$
re-arranging
$(T_{1}1/T_{2}) =(p_{1}/p_{2})^((k-1)/k)$
$T_{2} = T_{1}(p_{2}/p_{1})^((k-1)/k)$
Substituting the values
We get
$T_{2} = 177K$
Initial speed $c_{1} = \sqrt(K_{1}RT_{1}$
Final speed $c_{2} = \sqrt(K_{2}RT_{2})$
$K_{1} =K_{2}$ , because of ideal gas behavior.
So the ratio $c_{1}/c_{2} = \sqrt(KRT_{1})/\sqrt(RT_{2})$
=$\sqrt(T_{1})/\sqrt(T_{2})$
substituting the values
$c_{1}/c_{2} = 1.41$
