Ncert Exercises & Solutions

Speed of sound wave in the air

1. is independent of temperature

2. increases with the pressure

3. increases with increase in humidity

4. decreases with increase in humidity

(3) Hint: The speed of the sound wave depends on the temperature and the density of the air.

Step 1: Find the dependence of the sound wave on the density of the air.

Due to the presence of moisture density of air decreases.

We Know that the speed of sound in air is given by, v=

\sqrt{\frac{γP}{ρ}}

For air

γ and P

are constants,

ν \propto \frac{1}{\sqrt{ρ}},

where

ρ

is the density of air.

\frac{ν_{2}}{ν_{1}} = \sqrt{\frac{ρ_{1}}{ρ_{2}}}

where

ρ_{1}

is the density of dry air and

ρ_{2}

is the density of moist air.

Step 2: Find the comparative speed of the sound in the moist air.

ρ_{2} < ρ_{1} = \frac{ν_{2}}{ν_{1}} > 1 \Rightarrow ν_{2} > ν_{1}

Hence, the speed of the sound wave in the air increases with an increase in humidity.