The ratio of the velocity of sound in hydrogen (γ=7/5 ) to that in helium (γ=5/3 ) at the same temperature is

Correct answer: (C) (√42)/5. Velocity of sound in a gas v=√((γ p)/d) fracv_H_2V_He=√fracγ_H_2 × d_Hed_H_2 × γ_He fracH_2He=√((7 × 3 × 2)/(5 × 5)) As fracd_Hed_H_2=2 ∴ fracv_H_2v_He=(√42)/5

Q172 / 180 · KCET 2007 · Physics

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

A
$\sqrt{\frac{5}{42}}$
B
$\sqrt{\frac{5}{21}}$
Correct answer
C
$\frac{\sqrt{42}}{5}$
D
$\frac{\sqrt{21}}{5}$

Solution

Velocity of sound in a gas $v=\sqrt{\frac{\gamma p}{d}}$ $\frac{v_{\mathrm{H}_{2}}}{V_{\mathrm{He}}}=\sqrt{\frac{\gamma_{\mathrm{H}_{2}} \times d_{\mathrm{He}}}{d_{\mathrm{H}_{2}} \times \gamma_{\mathrm{He}}}}$ $\frac{\mathrm{H}_{2}}{\mathrm{He}}=\sqrt{\frac{7 \times 3 \times 2}{5 \times 5}}$ $\begin{array}{ll}\text { As } \quad & \frac{d_{\mathrm{He}}}{d_{\mathrm{H}_{2}}}=2 \\ \therefore & \frac{v_{\mathrm{H}_{2}}}{v_{\mathrm{He}}}=\frac{\sqrt{42}}{5}\end{array}$

Hence, the correct answer is option: 'C'.

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

Solution

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