Discuss the effect of (i) Density (ii) humidity on the velocity of sound in gases?

Explanation

Effect of density: Consider two gases with different densities having same temperature and pressure. Then the speed of sound in the two gases are and
`v_(1) = sqrt((gamma_(1)P)/rho_(1))`………..(1)
and `v_(2) = sqrt((gamma_(2)P)/rho_(2))`……….(2)
Taking ratio of equation (1) and equation (2), we get
`v_(1)/v_(2) =(sqrt((gamma_(1)P)/rho_(1)))/(sqrt((gamma_(2)P)/rho_(2))) = sqrt((gamma_(1)rho_(2))/(gamma_(2)rho_(1)))`
For gases haviing same value of `gamma`.
`v_(1)/v_(2) = sqrt(rho_(2)/rho_(1))`.........(3)
Thus, the velocity of sound in a gas is inversely proportional to the square root of the density of the gas.
Effect of moisture (humidity): The density of moist air is 0.625 of that of dry ari, which means the presence of moisture in air(iincrease in humidity) decreases its density. Therefore, speed of sound increases with rise in humidity. From equation
`v = sqrt((gamma P)/rho) = sqrt(gamma cT)`.
`v= sqrt((gamma P)/rho)`.
Let `rho_(1), v_(1)` and `rho_(2),v_(2)` be the density and speeds of sound in dry air and moist air, respectively.
Since P is the total atmospheric pressure, According to Dalton's law of partial pressure it can be shown that
`rho_(2)/rho_(1) = P/(P_(1) + 0.625 P_(2))`
where `P_(1)` and `P_(2)` are the partial pressures of dry air and water vapour respectively. Then
`v_(1)=v_(2) sqrt(P/(P_(1) + 0.625 P_(2)))`

Effect of wind: The speed of sound is also affected by blowing of wind. In the direction along the wind blowing, the speed of sound increases whereas in the direction opposite to wind blowing, the speed of sound decreases.