Question

The velocity of sound in air is $330$ m/s. The r.m.s velocity of air molecules $(\gamma =1.4)$ is approximately equal to

• A. 400 m/s
• B. 471.4 m/s
• C. 231 m/s
• D. 462 m/s

Answer 1

Answer: (B)

471.4 m/s

$v_{air}=\sqrt{\frac{\gamma RT}{M}}=330m/s$

$v_{rms}=\sqrt{\frac{3RT}{M}}$

$=\sqrt{\frac{3}{\gamma }}\times 330m/s$

$\gamma =1.4$

$⟹v_{rms}=471.4m/s$