Question

On what properties of the medium, the velocity of sound depends?

Answer 1

The velocity of sound:

The velocity of sound in air ($V$) can be given by the formula as shown-

$V=\sqrt{\raisebox{1ex}{$\gamma P$}\!\left/ \!\raisebox{-1ex}{$\rho $}\right.}$

Here $\gamma$ represents the ratio of specific heats, which is equal to 1.4 for air.

$P$ represent the pressure of the air.

$\rho$ represent the density of the air.

1. Effect of pressure - As the pressure ($P$) of the air increase the density of air also increase so the value of $\frac{P}{\rho }$ the ratio remains the same, so on changing pressure velocity of sound does not change.
2. Effect of Temperature- As the temperature of air increase it expands so the density of air $\rho$decrease, which make an increase in the velocity of the sound and vice versa.
3. Effect of humidity- As the humidity of air increases the density $\rho$ of air decreases. Hence speed of sound increases and as the humidity of air decrease its density increase which decreases the velocity of sound.
4. Effect of density- As density ($\rho$) of air increases the speed of sound decreases and as density ($\rho$) of air decreases the speed of sound increases.
5. Effect of frequency- Velocity of the sound wave does not depend on frequency.

Hence, these are the factors on which the speed of sound depends.