Question

If at same temperature and pressure, the densities for two diatomic gases are $d_{1}and{d}_2$ respectively, then the ratio of velocities of sound in these gases will be

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

Answer 1

The correct option is A $\sqrt{\left(\frac{d_2}{d_1}\right)}$

As, $v=\sqrt{\frac{\gamma P}{d}}$
$\therefore v\propto \frac{1}{\sqrt{d}}$
$\therefore \frac{v_1}{v_2}=\sqrt{\frac{d_2}{d_1}}$