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JEE MainPhysicsWaves and Sound

Two sound waves propagating in a gas are described by their angular wave numbers k₁ = 4.00 rad/m and k₂ = 4.04 rad/m . If these two waves produce 21 beats in 3 s , the velocity of sound in the gas is

Options

  1. A1050 m s ⁻¹
  2. B175 m s ⁻¹
  3. C175 m s ⁻¹
  4. D350 m s ⁻¹

Correct answer

D. 350 m s ⁻¹

Step-by-step solution

The beat frequency is the number of beats per second: f_b = 21 3 = 7 Hz The frequency of a wave is related to its wave speed v and angular wave number k by f = vk 2 . For the two waves, the frequencies are: f₁ = v(4.00 ) 2 = 2.00v f₂ = v(4.04 ) 2 = 2.02v The beat frequency is the difference between the two frequencies: f_b = f₂ - f₁ 7 = 2.02v - 2.00v 7 = 0.02v Solving for the velocity v : v = 7 0.02 = 350 m s ⁻¹ Answer: 350 m s ⁻¹

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