Question

If speed of sound in gas is $k$ times the RMS speed of gas molecules, then $k$ is equal to

• A. $\sqrt{\frac{3}{2}}$
• B. $\sqrt{\frac{\gamma }{3}}$
• C. $\sqrt{\frac{3\gamma }{5}}$
• D. $\sqrt{\frac{\gamma }{2}}$

Answer 1

The correct option is B $\sqrt{\frac{\gamma }{3}}$

$\frac{V_s}{V_{rms}}=\frac{\sqrt{\frac{\gamma RT}{M}}}{\sqrt{\frac{3RT}{M}}}=\sqrt{\frac{\gamma }{3}}$