Question

The speed sound in a gas is $v$ the rms velocity of gas molecules is (c), if $\frac{C_p}{C_v}=\gamma$ for the gas then the ratio of $v$ to $c$ is

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

Answer 1

Answer: (D)

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

$\text{Solution}:$

Speed of sound $v_s=v=\sqrt{\frac{\gamma RT}{M_0}}$

rms speed $v_{rms}=c=\sqrt{\frac{3RT}{M_0}}$

$\frac{v}{c}=\sqrt{\frac{\gamma }{3}}$

$\text{Hence D is the correct option}$