Question

Use the formula v = (√ργ/ρ) to explain why the speed of sound in air increases with humidity.

Answer 1

speed of sound is given by $v=\sqrt{\frac{\gamma P}{\rho}}$
where v is the speed of sound in air,
$\gamma$ is adiabatic coefficient
P is pressure and $\rho$ is density

actually, density of moist air is less than density of dry air. or you can say that if humidity increases, density of air decreases.
but in a above formula, we know speed of sound is inversely proportional to square root of density of sound in air.

hence, speed of sound increase with humidity due to decrease density.