Answer
$c_{1}/c_{2} = 1.28$
Work Step by Step
we have
Initail speed $c_{1} = \sqrt(K_{1}RT_{1})$
Final speed $ c_{2} = \sqrt(K_{2}RT_{2})$
so
$c_{1}/c_{2} = \sqrt(KRT_{1})/\sqrt(KRT_{2})$
$K_{1} =K_{2}$ , since the air has ideal gas behavior
$ c_{1}/c_{2} = \sqrt(T_{1})/\sqrt(T_{2})$.........(1)
but$ (T_{1}1/T_{2}) =(p_{1}/p_{2})^((k-1)/k)$
so substituting for $(T_{1}1/T_{2})$ in eq(1)
we get
$c_{1}/c_{2} = \sqrt((p_{1}/p_{2})^((k-1)/k))$
given that p1 = 2.2
p2 = 0.4
K = 1.4
sustituting the values we get
$c_{1}/c_{2} =\sqrt((2.2/0.4)^((1.4-1)/1.4))$
$c_{1}/c_{2} = 1.28$
