Use the formula `v = sqrt(( gamma p )/(rho ))` to explain why the speed of sound in air increases with humidity.

Explanation

Effect of humidity `:`
We known, `v = sqrt(( gamma p )/( rho ))` i.e., `v prop (1)/( sqrt( rho ))`
Amount of water vapour content in the air is called humidity. Density of moist air is `((5)/(8))` of density of dry air.
As humidity increases, density of air decreases so that velocity of sound increases
We known that, `v_(d) prop ( 1)/( sqrt( rho_(d))) ` and `v_(m) prop ( 1)/( sqrt( rho _(m)))`
so that `(v_(m))/( v_(d)) = sqrt((rho_(d))/(rho_(m)))`
and `v_(m)= v_(d)sqrt((rho_(d))/(rho_(m)))` since `rho_(d) gt rho_(m), ( rho_(d))/(rho_(m))gt1`
hence `v_(m) gt v_(d) ` i.e., velocity of sound in moist air is greater than in dry air.