If the speed of sound through hydrogen is 1280 m/s, what will be the speed of sound (in m/s) through a mixture of 4 parts by volume of hydrogen and 1 part of oxygen? Given density of oxygen is 16 times that of hydrogen

If V is the volume of the mixture,

Volume of hydrogen $=\frac{4}{5}\mathrm{V}$

And volume of oxygen $=\frac{1}{5}\mathrm{V}$

Mass of oxygen $=\frac{1}{5}{\mathrm{V\rho }}_{\mathrm{O}}=\frac{\mathrm{V}}{5}\left(16{\mathrm{\rho }}_{\mathrm{H}}\right)\left(\text{ as }{\mathrm{\rho }}_{\mathrm{O}}=16{\mathrm{\rho }}_{\mathrm{H}}\right)$

Total mass of the mixture, ${\mathrm{m}}_{\text{mix }}=\frac{4}{5}{\mathrm{V\rho }}_{\mathrm{H}}+\frac{\mathrm{V}}{5}\left(16{\mathrm{\rho }}_{\mathrm{H}}\right)=4{\mathrm{V\rho }}_{\mathrm{H}}$

Density of mixture, ${\mathrm{\rho }}_{\mathrm{m}}=\frac{4{\mathrm{V\rho }}_{\mathrm{H}}}{\mathrm{V}}=4{\mathrm{\rho }}_{\mathrm{H}}$

Thus, $\frac{{\mathrm{v}}_{\mathrm{m}}}{{\mathrm{v}}_{\mathrm{H}}}=\sqrt{\frac{{\mathrm{\rho }}_{\mathrm{H}}}{{\mathrm{\rho }}_{\mathrm{m}}}}=\sqrt{\frac{1}{4}}=\frac{1}{2}$

or ${\mathrm{v}}_{\mathrm{m}}=\frac{1}{2}{\mathrm{v}}_{\mathrm{H}}=\frac{1}{2}\times 1280=640 \mathrm{m}/\mathrm{s}$