Question

If at same temperature and pressure, the densities for two diatomic gases are $d_1\text{and}{d}_2$ respectively, then the ratio of velocities of sound in these gases will be

• A. $\sqrt{\frac{d_2}{d_1}}$
• B. $\sqrt{\frac{d_1}{d_2}}$
• C. $\sqrt{d_1{d}_2}$
• D. $d_1{d}_2$

Answer 1

The correct option is A $\sqrt{\frac{d_2}{d_1}}$

Speed of sound $v=\sqrt{\frac{\gamma P}{d}}$

$\Rightarrow \frac{v_1}{v_2}=\sqrt{\frac{d_2}{d_1}}(\because P-\text{constant})$