Physics - Sound Wave Question with Solution | TestHub

$\begin{array}{l}\text{Here, }{\mathrm{v}}_{{\mathrm{H}}_2}=1328\mathrm{m}{\mathrm{s}}^{-1};{\mathrm{\rho }}_{{\mathrm{H}}_2}=\frac{{\mathrm{\rho }}_{\mathrm{air}}}{16};\mathrm{v}=\sqrt{\frac{\mathrm{\gamma P}}{\mathrm{8}}}\\ \\ {\text{Let v}}_{\text{air}}\text{\hspace{0.17em}be\hspace{0.17em}the\hspace{0.17em}velocity\hspace{0.17em}of\hspace{0.17em}sound\hspace{0.17em}in\hspace{0.17em}air\hspace{0.17em}at\hspace{0.17em}N.T.P}\\ \\ \mathrm{Now},\frac{{\mathrm{v}}_{\mathrm{air}}}{{\mathrm{v}}_{{\mathrm{H}}_2}}=\sqrt{\frac{{\mathrm{\rho }}_{{\mathrm{H}}_2}}{{\mathrm{\rho }}_{\mathrm{air}}}}\left\{\begin{array}{l}\text{Since }\\ {\mathrm{\gamma }}_{{\mathrm{H}}_2}={\mathrm{\gamma }}_{\mathrm{air}}\end{array}\right\}\\ \\ \mathrm{or}{\mathrm{v}}_{\mathrm{air}}={\mathrm{v}}_{{\mathrm{H}}_2}\sqrt{\frac{{\mathrm{\rho }}_{{\mathrm{H}}_2}}{{\mathrm{\rho }}_{\mathrm{air}}}}\\ \\ \mathrm{or}{\mathrm{v}}_{\mathrm{air}}=1328\sqrt{\frac{\frac{{\mathrm{\rho }}_{\mathrm{air}}}{16}}{{\mathrm{\rho }}_{\mathrm{air}}}}=1328\sqrt{\frac{1}{16}}=\frac{1328}{4}\\ \\ {\text{\hspace{0.17em}v}}_{\mathrm{air}}=332\mathrm{m}{\mathrm{s}}^{-1}\end{array}$