Physics : Waves - Solved Example Problems for Propagation of Sound Waves

The ratio of the densities of oxygen and nitrogen is 16:14. Calculate the temperature when the speed of sound in nitrogen gas at 17°C is equal to the speed of sound in oxygen gas.

From equation (11.25), we have

Where, R is the universal gas constant and M is the molecular mass of the gas. The speed of sound in nitrogen gas at 17°C is

Similarly, the speed of sound in oxygen gas at *t* in *K* is

Given that the value of *γ* is same for both the gases, the two speeds must be equal. Hence, equating equation (1) and (2), we get

Squaring on both sides and cancelling *γ R* term and rearranging, we get

Since the densities of oxygen and nitrogen is 16:14,

Substituting equation (5) in equation (3), we get

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