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KVPY2020PhysicsWave Optics

A student is jogging on a straight path with the speed 5 . 4   km per hour. Perpendicular to the path is kept a pipe with its opening 8   m from the road (see figure). Diameter of the pipe is 0 . 45   m At the other end of the pipe is a speaker emitting sound of 1280   Hz towards the opening of the pipes. As the student passes in front of the pipe, she hears the speaker sound for T seconds. T is i

Options

  1. A6 - 12
  2. B12 - 18
  3. C3 - 6
  4. D18 - 22

Correct answer

A. 6 - 12

Step-by-step solution

λ = 320 1280 = 0 . 25   m Using concept of diffraction of wave b sin θ = 1 . 22 λ sin θ = 25 45 × 1 . 22 = 0 . 678 tan θ = 0 . 93 tan θ = y 2 D y ⇒ 2 Dtan θ time to cross this region = 2 D tan θ  speed  ⇒ 2 × 8 × 0 . 93 1 . 5 ≃ 9 . 9 sec

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