Question

What is the effect of humidity on the quality of sounds propagation of sound in the air during the summer and winter seasons? Discuss.

Answer 1

Hint: Use the formula for the speed of sound in air. When the humidity in the air increases, the density of the air decreases. During the summer season, the density of air decreases, and during the winter season the density increases.
Formula used:
$v=\sqrt{\dfrac{\gamma P}{\rho }}$

Complete step-by-step solution:
We all know what sound is. Sound is a wave produced due to the vibration of air molecules. For example, when a stretched membrane like a drum is hit with a stick, it vibrates and also vibrates the surrounding air molecules. This way a sound is formed.
We know that a wave has a speed of propagation. Therefore, sound waves also have their speed of propagation. The speed of the sound waves depends on the pressure and the density of the air.
The speed of the sound is given as $v=\sqrt{\dfrac{\gamma P}{\rho }}$ …. (i).
Here, $\gamma $ is adiabatic constant, P is the pressure of air, and $\rho $ is the density of the air.
Let us discuss what happens to the speed of sound due to the humidity of air during the summer and winter seasons.
During the summer season, the temperature is higher. As a result, water easily evaporates, and the humidity in the air increases. However, since the temperature is high, the kinetic motion of the molecules increases. Hence, the volume of air increases.
We know that volume is inversely proportional to density. Therefore, on the expansion of volume the density of the air decreases. From equation (i) we get that speed of sound is inversely proportional to the density of air. Therefore, on a summer day speed of sound increases.
During winter, the temperature is low. As a result, the density of air is higher than that of during summer. Therefore, the speed of sound is less than that of the summer season.

Note: When the humidity of air increases, the water vapors in the air increase. Therefore, one may argue that if the water vapors are increasing the mass will increase, and thus the density will increase. However, when the water vapors increase, the mass of air molecules decreases and thus the density decreases.