Write down the factors affecting velocity of sound in gases.

Explanation

Effect of density: Let us consider two gases with different densities having same temperature and pressure. Then the speed of sound in the two gases are
`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))))/((gamma_(2)P)/(rho_(2))) = sqrt((gamma_(1)rho_(2))/(gamma_(2)rho_(1)))`
For gases having same value of `gamma`.
`(v_(1))/(v_(2)) = sqrt((rho_(2))/(rho_(1)))`
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): We know that density of moist air is 0.625 of that of dry air, which means the presence of moisture in air (increase in humidity) decreases its density. Therefore, speed of sound increases with rise in humidity. From equation:
v `= sqrt((gammarho)/(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.
Then
`(v_(1))/(v_(2)) = (sqrt((gamma_(1)P)/(rho_(1))))/(sqrt((gamma_(2)P)/(rho_(2)))) = sqrt((rho_(2))/(rho_(1)))` if `r_(1) = r_(2)`
Since P is the total atmospheric 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)))`