Velocity of sound waves in air

Introduction:
The velocity of sound waves in air is influenced by various factors, including temperature. The relationship between temperature and the velocity of sound waves in air can be explained by the molecular motion and the resulting changes in air density.

Variation of sound velocity with temperature:
The velocity of sound waves in air varies directly as the square root of absolute temperature. This means that as the temperature increases, the velocity of sound waves in air also increases, and vice versa.

Explanation:
- Direct variation: The velocity of sound waves in air is directly proportional to the square root of the absolute temperature. This implies that if the temperature doubles, the velocity of sound waves will also double.

- Square root relationship: The square root relationship arises from the molecular motion of air molecules. As the temperature increases, the air molecules gain kinetic energy and move faster. This leads to an increase in the speed of sound waves.

- Absolute temperature: The use of absolute temperature (measured in Kelvin) is important in this relationship. Absolute temperature is the temperature measured from the absolute zero point, where molecular motion theoretically stops. In this scale, zero Kelvin represents the absence of molecular motion.

- Inversely proportional: The square root relationship between the velocity of sound waves and absolute temperature means that the velocity varies inversely as the square root of absolute temperature. As the temperature increases, the square root of absolute temperature also increases, resulting in a higher velocity of sound waves.

- Constant proportionality: The constant of proportionality between the velocity of sound waves and the square root of absolute temperature is dependent on the properties of the medium through which the sound waves propagate. In the case of air, this constant is approximately 331 m/s at 0 degrees Celsius.

- Experimental verification: The relationship between temperature and the velocity of sound waves in air has been experimentally verified. As the temperature of the air increases, the speed of sound waves also increases, which can be observed in various phenomena, such as the difference in pitch of a siren on a hot day compared to a cold day.

In conclusion, the velocity of sound waves in air varies directly as the square root of absolute temperature. This relationship arises from the molecular motion of air molecules and the resulting changes in air density.