alleryStart learning →Velocity of sound in an ideal gas is $v_s = \sqrt{\gamma RT/M_0}$. Compared to rms speed, $v_s$:
- Equals $v_{rms}$ always
- Is smaller than $v_{rms}$ (since $\gamma \le 5/3 < 3$)
- Is larger than $v_{rms}$
- Can be zero
Show answer and solution
Correct answer: B. Is smaller than $v_{rms}$ (since $\gamma \le 5/3 < 3$)
$v_s/v_{rms} = \sqrt{\gamma/3}$.
Since $\gamma \le 5/3 < 3$, $v_s < v_{rms}$ always.
(Sound waves can't propagate faster than the molecules they ride on.) For monatomic gas, ratio = $\sqrt{5/9} \approx 0.745$.