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COMEDK2023Morning ShiftPhysicsWaves and SoundActual

A car is moving towards a high cliff. The car driver sounds a horn of frequency f . The reflected sound heard by the driver has a frequency 2 f . If v be the velocity of sound, then the velocity of the car in the same velocity units, will be

Options

  1. Av 3
  2. Bv 2
  3. Cv 4
  4. Dv 2

Correct answer

A. v 3

Step-by-step solution

Let v_c be the velocity of the car and v be the velocity of sound. The frequency of sound heard by the cliff (stationary observer) is f' = f ( v v - v_c ) . The cliff acts as a source reflecting this frequency f' back to the moving car (moving observer). The frequency f'' heard by the driver is f'' = f' ( v + v_c v ) . Substituting f' into the equation for f'' , we get f'' = f ( v v - v_c ) ( v + v_c v ) = f ( v + v_c v - v_c ) . Given that the reflected sound heard by the driver is 2f , we have 2f = f ( v + v_c v

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