The speed of sound in air is directly related to the air temperature at a particular altitude. The relationship between the speed of sound (c), air temperature (T), and altitude can be expressed by the following simplified formula:
c = √(γ * R * T)
Where:
c is the speed of sound in air.
γ (gamma) is the adiabatic index or the heat capacity ratio of the air (approximately 1.4 for dry air).
R is the specific gas constant for dry air (approximately 287 J/(kg·K)).
T is the absolute temperature in Kelvin (K).
In this formula, the speed of sound (c) is proportional to the square root of the absolute temperature (T) in Kelvin. This means that as air temperature increases, the speed of sound also increases, and as temperature decreases, the speed of sound decreases.
At different altitudes, air temperature can vary, and this variation affects the speed of sound. In general, the speed of sound is lower at higher altitudes because the air is cooler at higher elevations. As you move upward in the Earth’s atmosphere, both temperature and air pressure decrease, leading to a decrease in the speed of sound.
It’s important to note that this is a simplified formula, and the actual relationship between speed of sound and temperature in the atmosphere is influenced by other factors like humidity and the composition of the air. Nevertheless, this formula provides a useful approximation for understanding the relationship between speed of sound and temperature in air.
