Speed of sound increases as temperature increases because molecules at higher temperatures have more energy and can vibrate faster, allowing sound waves to travel more fast.
The relationship between temperature and the speed of sound can be explained by the kinetic theory of gases. According to this theory, temperature is related to the average kinetic energy of gas molecules.
As the temperature increases, the air molecules gain more kinetic energy and move faster. In a sound wave, the speed of sound is determined by how quickly molecules can transmit the disturbance (compression and rarefaction) through the medium. In warmer air, where molecules are moving faster on average, sound waves can be transmitted more quickly, resulting in an increase in the speed of sound.
The relationship between temperature (T) and the speed of sound (v) in air can be approximated by the following equation:
v ≈ √γ × R × T
where:
- v is the speed of sound,
- γ is the adiabatic index (ratio of specific heat at constant pressure to specific heat at constant volume),
- R is the gas constant,
- T is the temperature in kelvin.