17.5:
Speed of Sound in Gases
When a sound wave passes through a gas column, no heat is exchanged between the wave and the gaseous constituents.
Using the continuity equation of fluid mechanics, Newton's second law of motion, the definition of density, and the equations from thermodynamics, the speed of sound in a gas can be deduced. It depends on the composition of the gas and its temperature.
The speed of sound through any gas can be numerically estimated by substituting its known properties in the equation relating the quantities.
At a temperature of 0° C, the speed of sound in air is 331 meters per second. At the same temperature, it is 259 meters per second in carbon dioxide and 1254 meters per second in hydrogen gas.
The speed of sound in air is independent of the frequency of the propagating sound wave. Hence, a band of musicians playing instruments at different pitches appears in perfect sync.
17.5:
Speed of Sound in Gases
The speed of sound in a gaseous medium depends on various factors. Since gases constitute molecules that are free to move, they are highly compressible. Hence, sound waves travel slowly through gases. Thermodynamics helps us understand the relationship between pressure, volume, and temperature of gases, thus, the speed of sound in an ideal gas can be determined using the laws of thermodynamics. At the same time, Newton's laws of motion and the continuity equation of fluid dynamics also come in handy.
The speed of sound in a gas depends on the universal gas constant and the properties of the particular gas. The speed of sound depends on the gaseous constituents. It also changes with the temperature of the gas. However, this change is not drastic as the speed changes with the square root of the temperature. For example, the speed of sound in air at 20 °C is only 4% more than the speed of sound in air at 0 °C.
The speed of sound in air does not depend on the frequency of the sound. If it did, our perception of sound would be different, as familiar sources of sound are a linear superposition of sounds of different frequencies.
This text is adapted from Openstax, University Physics Volume 1, Section 17.2: Speed of Sound.