Question

Speed of sound in moist air is ___________ than speed of sound in dry air:
A) Less
B) Same as
C) More
D) Data insufficient

Answer 1

Hint: In order to solve this consider the pressure and temperature conditions. Always remember that the density of water vapour is less than the density of dry air at ordinary temperature. Remember the relation between the speed of sound in moist air and the speed of sound in dry air.

Complete step by step solution:
We know that the formula for the speed of sound in air is given by,
$V = \sqrt {\dfrac{{\gamma P}}{d}} $
Where $\gamma = \dfrac{{{C_P}}}{{{C_v}}}$
$P$ is the pressure
$d$ is the density

As we already know that the density of water vapour is less than the density of dry air at ordinary temperatures and it is in the ratio $0.62:1$.
Therefore, the presence of moisture in the air decreases the density of air and therefore increases the speed of sound in that moist air.
Hence, at a given temperature, the sound of air in moist air is more than the speed of sound in dry air.

Therefore, the correct option is (C).

Additional information:
The relation between the speed of sound in moist air and speed of sound in dry air is given by
${V_d} = {V_m}\sqrt {\left\{ {1 - \left( {\dfrac{{0.378f}}{P}} \right)} \right\}} $
Where ${V_d}$ is the speed of sound in dry air
${V_m}$ is the speed of sound in moist air
$f$ is the saturation pressure of moisture at given temperature
$P$ is the pressure of the air

Note: The speed of sound in dry air is $340m/s$ whereas the speed of sound in moist air is $346m/s$. Keep in mind that the water vapour is lighter than dry air. As we remove the moisture from air, then its density increases and the speed of sound in moist air is inversely proportional to the root of its density.