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The ratio of the velocity of sound in hydrogen $\left(\gamma=\frac{7}{5}\right)$ to that in helium $\left(\gamma=\frac{5}{3}\right)$ at the same temperature is
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$\frac{\sqrt{42}}{5}$
Velocity of sound in a gas
$v=\sqrt{\frac{\gamma p}{d}}$
$\frac{v_{\mathrm{H}_{2}}}{V_{\mathrm{He}}}=\sqrt{\frac{\gamma_{\mathrm{H}_{2}} \times d_{\mathrm{He}}}{d_{\mathrm{H}_{2}} \times \gamma_{\mathrm{He}}}}$
$\frac{\mathrm{H}_{2}}{\mathrm{He}}=\sqrt{\frac{7 \times 3 \times 2}{5 \times 5}}$
$\begin{array}{ll}\text { As } \quad & \frac{d_{\mathrm{He}}}{d_{\mathrm{H}_{2}}}=2 \\ \therefore & \frac{v_{\mathrm{H}_{2}}}{v_{\mathrm{He}}}=\frac{\sqrt{42}}{5}\end{array}$
$v=\sqrt{\frac{\gamma p}{d}}$
$\frac{v_{\mathrm{H}_{2}}}{V_{\mathrm{He}}}=\sqrt{\frac{\gamma_{\mathrm{H}_{2}} \times d_{\mathrm{He}}}{d_{\mathrm{H}_{2}} \times \gamma_{\mathrm{He}}}}$
$\frac{\mathrm{H}_{2}}{\mathrm{He}}=\sqrt{\frac{7 \times 3 \times 2}{5 \times 5}}$
$\begin{array}{ll}\text { As } \quad & \frac{d_{\mathrm{He}}}{d_{\mathrm{H}_{2}}}=2 \\ \therefore & \frac{v_{\mathrm{H}_{2}}}{v_{\mathrm{He}}}=\frac{\sqrt{42}}{5}\end{array}$
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