The speed of sound in hydrogen at $NTP$ is $1270\,m/s$ . Then, the speed in a mixture of hydrogen and oxygen in the ratio $4 : 1$ by volume will be ..... $m/s$
Diffcult
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Suppose $V$ be the volume of oxygen. The volume of hydrogen will be $4 \mathrm{V}$. If $\rho_{\mathrm{m}}$ be the density of the mixture, then
$\rho_{\mathrm{m}}=\frac{4 \mathrm{V} \times 1+\mathrm{V} \times 16}{5 \mathrm{V}}=4$
i.e., density of mixture is 4 times that of hydrogen. $\mathrm{As}$
$\mathrm{V} \propto(1 / \rho)^{1 / 2}$
Velocity in mixture $=\frac{1270}{(4)^{1 / 2}}=635 \mathrm{\,m} / \mathrm{s}$
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