Question

In which medium does a sound wave travel faster: in cool air or in warm air?

Short answer

Answer: Sound travels faster in warm air compared to cool air. This is because the speed of sound in a medium is directly proportional to the square root of its temperature, and in warmer air, gas molecules have more kinetic energy which leads to a higher speed of sound.

Step-by-step solution

1. Understand the speed of sound in a medium

The speed of sound in a medium, such as air, depends on the properties of the medium like its density and elastic properties. Temperature affects these properties, and therefore, influences the speed of sound.

2. Relationship between temperature and speed of sound

The speed of sound in a medium is given by the formula: v = sqrt(K/ρ), where v is the speed of sound, K is the bulk modulus of the medium, and ρ is the density of the medium. For an ideal gas, such as air, the speed of sound can be determined using the formula: v = sqrt(γRT/M), where γ is the adiabatic index, R is the gas constant, T is the absolute temperature, and M is the molar mass of the gas. This relationship demonstrates that the speed of sound in an ideal gas is proportional to the square root of its temperature.

3. Analyze the effect of temperature on the speed of sound

As the temperature increases, the speed of sound in the gas also increases, and vice versa. This is because, in warmer air, the gas molecules have more kinetic energy and bounce around more quickly, leading to a higher pressure and speed of sound. In cooler air, these gas molecules move slower, resulting in a slower speed of sound.

4. Determine which medium the sound travels faster

Based on the relationship between temperature and the speed of sound in a medium, a sound wave travels faster in warm air than in cool air.