When the pressure of air is doubled at a constant temperature, the velocity of sound in the air remains unchanged. The speed of sound in a gas is determined by the properties of the medium, such as its density and elasticity, rather than the pressure alone.
According to the ideal gas law, when pressure is doubled at a constant temperature, the density of the gas also doubles, assuming no change in the other gas properties. As a result, the increased density compensates for the increased pressure, and the velocity of sound in the air remains the same.
The speed of sound in a specific medium can be calculated using the equation:
v = √(γ * P / ρ)
Where: v = velocity of sound γ = adiabatic index (specific heat ratio) of the gas P = pressure of the gas ρ = density of the gas
Since both pressure (P) and density (ρ) increase proportionally when the pressure is doubled, the ratio (P / ρ) remains constant. Therefore, the velocity of sound (v) does not change.