### Theory:

Factors affecting the velocity of sound:
The velocity of sound waves is affected by the elastic properties and density of solids when the sound wave travels in the solid medium. Their elastic moduli characterise the elastic property of solids. The velocity of sound is directly proportional to the square root of the elastic modulus and inversely proportional to the square root of the density. As a result, as the density of solid increases, the velocity of sound decreases, whereas as the elasticity of the material increases, the velocity of sound increases.

The velocity of sound waves in gases is affected by the following factors.
• Effect of Density
• Effect of temperature
• Effect of relative humidity
Effect of density:

In a gas medium, the velocity of sound is inversely proportional to the square root of the density. As a result, as the density of the gas increases, the velocity decreases.

Effect of temperature:

In a gas medium, the velocity of sound is proportional to the square root of the temperature $v\propto \sqrt{T}$. The velocity of sound in a gas increases as the temperature increases.

The following equation gives the velocity at temperature $$T$$:

${v}_{t}=\left({v}_{0}+0.61\phantom{\rule{0.147em}{0ex}}T\right)$

Here, ${v}_{0}$ is the velocity of sound in the gas medium at $$0° C$$.

For air, ${v}_{0}$ $$=$$ $$331$$ $m/s$

Hence, the velocity of sound changes by $$0.61$$ $m/s$ when the temperature changes by one degree Celsius.

Effect of relative humidity:

The speed of sound increases as humidity rises. That is why, during rainy seasons, you can clearly hear sounds from a long distance.