The speed of sound in air is directly proportional to the temperature of the air. This means that as the temperature increases, the speed of sound also increases, and vice versa. This relationship is known as the "direct proportionality" of temperature and speed of sound in air.
Humidity does have an effect on the speed of sound in air, but it is not as significant as temperature. As humidity increases, the speed of sound decreases slightly due to the water vapor in the air, which makes it harder for sound waves to travel. However, this effect is very small and is often not noticeable in everyday situations.
The formula for calculating the speed of sound in air is: c = √(γRT), where c is the speed of sound, γ is the adiabatic index of air (which is approximately 1.4), R is the gas constant for air (approximately 287 J/kg.K), and T is the temperature in Kelvin. This formula is known as the Newton-Laplace equation.
Sound travels faster in warm air because the molecules in warm air are moving at a higher speed compared to cold air. This means that sound waves can travel through warm air more quickly and efficiently, resulting in a higher speed of sound.
The speed of sound in air is also affected by altitude. As altitude increases, the speed of sound decreases due to the lower air density. This means that sound waves have less molecules to travel through, resulting in a slower speed of sound. This is why sound travels faster at sea level compared to higher altitudes.