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.

Answer

Assume ideal gas law : `P = (rhoRT)/(M)` where `rho` is the density, `M` is the molecular mass, and `T` is the temperature of the gas. This gives `v = sqrt((gammaRT)/(M))`. This shows that `v` is
(a) Independent of pressure.
(b) Increase as `sqrt(T)`.
(c) The molecular mass of water `(18)` is less then that of `N_(2) (28)` and `O_(2)(32)`. Therefore as humidity increases, the effective molecular mass of air decrease and hence `v` increases.