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A sound wave of frequency f travelling horizontally to the right is reflected by a large vertical plane surface moving to left with a speed v . There is a detector ( 1 ) attached on the surface and another detector ( 2 ) fixed on ground. If the speed of sound in the medium is c , then the difference in the frequency received by detector 2 after being reflected from the surface and the frequency received by detector 1

Options

  1. A∆ f = f c c - v v c + v
  2. B∆ f = f v c - v c c + v
  3. C∆ f = f c c + v v c - v
  4. D∆ f = f v c + v c c - v

Correct answer

D. ∆ f = f v c + v c c - v

Step-by-step solution

f 1 = f c + v c f 2 = f 1 c c - v = f c + v c - v ∆ f = f c + v c - v - c + v c ∆ f = f c c + v - c - v c + v c c - v ∆ f = f c 2 + c v - c 2 - v 2 c c - v ∆ f = f v c + v c c - v

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