NCERT Class 11 Physics Solutions: Chapter 15 – Waves-Part 2

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Question 15.4:

Use the formula to explain why the speed of sound in air is independent of pressure, increases with temperature, and increases with humidity.

Answer:

Take the relation:

Where,

Density,

Molecular weight of the gas

Volume of the gas

Hence, Equation reduce to:

Now from the ideal gas equation for

For constant Constant

Since both are constants,

Constant

Hence, at a constant temperature, the speed of sound in a gaseous medium is independent of the change in the pressure of the gas.

Take the relation:

For one mole of an ideal gas, the gas equation can be written as:

Substituting equation in equation , we get:

Where,

Mass, is constant

are also constants

We conclude from equation that

Hence, the speed of sound in a gas is directly proportional to the square root of the temperature of the gaseous medium, i.e., the speed of the sound increases with an increase in the temperature of the gaseous medium and vice versa.

Let be the speeds of sound in moist air and dry air respectively.

Let be the densities of moist air and dry air respectively.

Take the relation:

Hence, the speed of sound in moist air is:

And the speed of sound in dry air is:

On dividing equations we get:

However, the presence of water vapor reduces the density of air, i.e.

Hence, the speed of sound in moist air is greater than it is in dry air. Thus, in a gaseous medium, the speed of sound increases with humidity.