The ratio of densities of oxygen and nitrogen at a given temperature is 16 : 14. The ratio of speed of sound in oxygen and nitrogen at that temperature is

The speed of sound in a gas is given by the formula v = √(γP/ρ), where γ is the adiabatic constant, P is the pressure, and ρ is the density.

For a given temperature and pressure, the speed of sound in a gas is inversely proportional to the square root of the density of the gas. This is because γ and P are constant for a given temperature and pressure, so the formula simplifies to v ∝ 1/√ρ.

Given the ratio of densities of oxygen and nitrogen is 16 : 14, the ratio of speeds of sound in oxygen and nitrogen is the inverse ratio of the square roots of their densities.

So, the ratio of speeds of sound in oxygen and nitrogen is √14 : √16 = 7/4 : 4/4 = 7 : 4.