Why does sound travel slower in cooler air?

Sound travels slower in cooler air because the molecules are less energetic and move slower, reducing the speed of sound propagation.

In more detail, the speed of sound in a medium is determined by the properties of that medium. In the case of air, these properties include temperature, humidity, and atmospheric pressure. However, temperature is the most significant factor affecting the speed of sound in air.

When air is heated, the molecules gain energy and move faster. This increased molecular motion allows sound waves to be transmitted more quickly. Conversely, when the air is cooled, the molecules lose energy and move slower. This reduced molecular motion slows down the transmission of sound waves.

The speed of sound is directly proportional to the square root of the absolute temperature. This relationship is described by the equation v = √γRT, where v is the speed of sound, γ is the adiabatic index (ratio of specific heats), R is the gas constant, and T is the absolute temperature.

As the temperature decreases, the value of √T also decreases, leading to a decrease in the speed of sound. For example, at 0°C, the speed of sound in dry air is approximately 331 m/s. However, at 20°C, the speed increases to about 343 m/s.

It's also worth noting that humidity and atmospheric pressure can also affect the speed of sound, but to a lesser extent than temperature. Humidity can actually increase the speed of sound, as water vapour is lighter than dry air and allows sound waves to travel faster. Atmospheric pressure has a negligible effect on the speed of sound in air, as changes in pressure are usually accompanied by changes in density that cancel each other out.

In conclusion, the speed of sound in air is primarily determined by the temperature of the air. Cooler air results in slower-moving molecules, which in turn slows down the propagation of sound waves.