From the formula $v = \sqrt{\frac{\gamma P}{\rho}}$, for an ideal gas at constant temperature, pressure P and density ρ are directly proportional to each other. When pressure changes, density changes proportionally, keeping the ratio P/ρ constant. Hence, the speed of sound is independent of pressure.

At higher temperatures, the gas expands and its density ρ decreases. Since velocity v is inversely proportional to the square root of density (v ∝ 1/√ρ) from the formula, a decrease in density causes an increase in velocity. Thus, the speed of sound increases with temperature.

Humid air contains water vapour which has lower molecular mass than dry air components. This results in lower density ρ for humid air compared to dry air. Since v ∝ 1/√ρ from the formula, lower density leads to higher speed. Therefore, the speed of sound increases with humidity.