Question

The speed of sound in a gas is $V$. If the rms velocity of gas molecules is C${}_{rms}$ then the value of $\frac{V}{C_{rms}}$ will be

• A. $\frac{3}{\gamma }$
• B. $\frac{\gamma }{3}$
• C. $\sqrt{\frac{3}{\gamma }}$
• D. $\sqrt{\frac{\gamma }{3}}$

Answer 1

Answer: (D)

$\sqrt{\frac{\gamma }{3}}$

Speed of sound $V=\sqrt{\frac{\gamma RT}{M}}$

rms velocity of gas molecules $C_{rms}=\sqrt{3\frac{RT}{M}}$

$\frac{V}{C_{rms}}=\sqrt{\frac{\gamma }{3}}$

Answer is D.