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Chapter: 11th Physics : Waves

Solved Example Problems for Propagation of Sound Waves

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

EXAMPLE 11.9

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.

Solution

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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