Question

If vm is the velocity of sound in moist air, vd is the velocity of sound in dry air under identical conditions of pressure and temperature.

Answer 1

Just like that the water vapor is lighter than dry air. When moisture is removed from air, its density increases). The speed of sound in a medium is inversely proportional to the square root of its density. Therefore, the speed of sound in moist air is more than that in dry air.

Answer 2

The velocity of sound in moist air is higher than the velocity of sound in dry air. hence option (2) is correct.

If vm is the velocity of sound in moist air, vd is the velocity of sound in dry air under identical condition of pressure and temperature.

Which of the following is the correct relation between vm and vd ?

1. $v_m < v_d$
2. $v_m > v_d$
3. $v_mv_d=1$
4. $v_m=v_d$

We know, the density of moist air is less than the density of dry air because the density of moist air has water which is lighter than the weight of nitrogen and oxygen in a specific volume.

$\implies \rho_d < \rho_m\:\:...(1)$

Now, The formula of velocity of sound is given by,

$v=\sqrt{\frac{\gamma P}{\rho}}$

Where,

• γ is adiabatic constant
• P is pressure.
• ρ is density.

By formula of velocity of sound, It is clear that the velocity is inversely proportional to the square root of the density under identical conditions of pressure and temperature.

$\implies v\propto\frac{1}{\sqrt{\rho}}\:\:...(2)$

From equations (1) and (2), It is clear that the velocity of sound in moist air is higher than the velocity of sound in dry air.

Therefore the correct option is (2).

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