The ratio of the speed of sound in nitrogen gas to that in h... | PHYSICS - REFLECTION OF WAVES | SolveeIt

Question

The ratio of the speed of sound in nitrogen gas to that in helium gas, at 300 K is

$\sqrt{2/7}$

$\sqrt{1/7}$

$\sqrt{3}/5$

$\sqrt{6}/5$

Answer

$\sqrt{3}/5$

Explanation

Solution

Velocity of sound in gas $v = \sqrt{\frac{\gamma RT}{M}}$ ⇒ $v \propto \sqrt{\frac{\gamma T}{M}}$

⇒ $\frac{v_{N_{2}}}{v_{He}} = \sqrt{\frac{\gamma_{N_{2}}}{\gamma_{He}} \times \frac{M_{He}}{M_{H_{2}}}} = \sqrt{\frac{\frac{7}{5}R \times 4}{\frac{5}{3}R \times 28}} = \frac{\sqrt{3}}{5}$

Question: The ratio of the speed of sound in nitrogen gas to that in helium gas, at 300 K is...

Solution