b
\(v_{s}=\sqrt{\frac{\gamma P}{\rho}}\)

\(\frac{\mathrm{v}_{\mathrm{gas}}}{\mathrm{v}_{\mathrm{air}}}=\sqrt{\frac{\rho_{\mathrm{air}}}{\rho_{\mathrm{gas}}}}\)

\(\Rightarrow \frac{\mathrm{v}_{\mathrm{gas}}}{300}=\frac{1}{\sqrt{2}}\)

\(\Rightarrow \mathrm{v}_{\mathrm{gas}}=\frac{300}{\sqrt{2}}\)

\(\therefore \mathrm{v}_{\mathrm{grs}}=150 \sqrt{2}\)

Now \(\mathrm{n}_{2}-\mathrm{n}_{1}=\frac{\mathrm{v}_{\mathrm{gss}}}{2 \ell}=\frac{150 \sqrt{2}}{2(1)}=75 \sqrt{2}\)

\(\Rightarrow \Delta \mathrm{n}=106.06 \mathrm{Hz}\)