Answer
$\gamma=1.40$
Work Step by Step
From ideal gas law, the speed of sound is given as;
$v_s=\sqrt\frac{\gamma RT}{M}$
This can be rearranged as:
$\gamma=\frac{Mv_s^2}{RT}$........eq(1)
Next, we find the wavelength:
$\lambda =2(9.57cm)=19.14cm=0.1914m$
As $v_s=f\lambda$,
$v_s=(1000)(0.1914)=191.5\frac{m}{s}$
Finally, we plug in known values in eq(1) we to obtain:
$\gamma=\frac{0.127(191.4)}{8.314(400)}=1.40$
