Question

The relation between speed of sound in moist air $v_m$ and dry air $v_d$ at the same temperature and pressure will be

• A. $v_m<v_d$
• B. $v_m>v_d$
• C. $v_m=v_d$
• D. $v_m\le v_d$

Answer 1

The correct option is B $v_m>v_d$

We know that the speed of sound in air is given by,
$v=\sqrt{\frac{\gamma P}{\rho }}=\sqrt{\frac{\gamma RT}{M}}$
At the same temperature and pressure of air,
$v\propto \frac{1}{\sqrt{M}}$ ..........(1)
Dry air mostly contains nitrogen$\left(78\%\right)$ and oxygen$(\simeq 21\%)$ gas and other gases like $C{O}_2$ in traces . Moist air will contain a higher volume fraction of the moisture. The moisture will replace some of the volume occupied by gases like $C{O}_2,N_2,O_2,\text{etc}$.
Molar mass of $H_{2}O$ is $18\text{g/mol}$, which is lesser than the constituent components of air.

This will lead to reduction in the effective molar mass of the moist air$(M_{\text{moist air}}<M_{\text{dry air}})$.

$\Rightarrow M_d>M_m$ .........(2)
From Eq. (1) and (2) the relation between velocity of sound is,
$v_m>v_d$