Factors Affecting Velocity of Sound in Gas

Effect of Temperature

From Laplace’s formula

v = √(γP/ρ)

Since density is ratio of mass per unit volume,

v = √(γPV/M)

Using the equation of state PV = nRT, where n is number of moles in mass m of the gas

v = √(γRT/m)

Where m denotes the gram molecular mass. This result shows that

v ∝ √T

For small temperature variations, velocity of sound in air increases by 0.61 ms^–1 with every degree celsius rise in temperature.

Effect of Pressure

When you increase pressure on a gas, it gets compressed but its density increases in the same proportion as the pressure i.e. P/ρ remains constant. It means that, pressure has no effect on the velocity of sound in a gas.

Effect of Density

If you consider two gases under identical conditions of temperature and pressure, then

v ∝ 1/√ρ

Effect of Humidity

As humidity in air increases (keeping conditions of temperature and pressure constant), its density decreases and hence velocity of sound in air increases.