Question

If $\upsilon_{s}$ is the velocity of sound in air and $\upsilon$ is the $rms$ value, then

• A. $\upsilon_{s} >\,\upsilon$
• B. $\upsilon_{s} =\upsilon$
• C. $\upsilon_{s} =\upsilon \left[\frac{\gamma}{3}\right]^{1 /2}$
• D. $\upsilon_{s} =\upsilon \left[\frac{3}{\gamma}\right]^{1 /2}$

Answer 1

Answer: (C)

$\upsilon_{s} =\upsilon \left[\frac{\gamma}{3}\right]^{1 /2}$

Answer 2

Velocity of sound in air is $v_{s}=\sqrt{\frac{\gamma P}{\rho}}\quad\ldots\left(i\right)$ Its $rms$ velocity is $v=\sqrt{\frac{3P}{\rho}}\quad\ldots\left(ii\right)$ Divide $\left(i\right)$ by $\left(ii\right)$, we get $\frac{v_{s}}{v}=\sqrt{\frac{\gamma}{3}}$ $v_{s}=\sqrt{\frac{\gamma}{3}}v$ or $v_{s} < v$