Use the formula `v=sqrt((gamma P)/(rho))` to explain why the speed of sound in air
(a) is independent of pressure, (b) increases with temperature, (c) increases with humidity.

Explanation

Given `v=sqrtgammap//p`
(a) Let V be the volume of 1 mole of air, then
`rho= M/V or V= M/P` for 1 mole of air `PV = RT`
`therefore (PM)/rho = RT or P/rho=(RT)/M
Rightarrow v=sqrt(gammaRT)/M` so at constant temperature v is constant as `gamma`,R and M are constant.
(b) From equation (i) we know that `VasqrtT`, so with the increase in temperature velocity of sound increases.