Which parameter does the acoustic velocity of a gas primarily vary with?

The acoustic velocity of a gas is primarily influenced by the absolute temperature of the gas. This is because the speed of sound in a gas is derived from the fundamental relationship between pressure, density, and temperature. According to the ideal gas law, as the temperature increases, the kinetic energy of the gas molecules increases, leading to greater speeds at which sound waves can propagate through the gas.

Mathematically, the speed of sound (c) in an ideal gas can be expressed as:

[

c = \sqrt{\frac{\gamma \cdot R \cdot T}{M}}

]

where:

• (c) is the speed of sound,

• (\gamma) is the ratio of specific heats,

• (R) is the specific gas constant,

• (T) is the absolute temperature,

• (M) is the molar mass of the gas.

From this equation, it is clear that the speed of sound is directly proportional to the square root of the absolute temperature. Thus, an increase in temperature will result in an increase in acoustic velocity, while a decrease will lead to a lower speed of sound.

While other parameters, such as the specific gas constant and the ratio of specific heats,