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NEET2017PhysicsWaves and SoundActual

A wave packet with center frequency is propagating in dispersive medium with phase velocity of 1.5 10^3 ~m / s . When the frequency is increased by 2 % , the phase velocity is found to decrease by 3 % . What is the group velocity of the wave packet?

Options

  1. A0.25 10^3 ~m / s
  2. B1.0 10^3 ~m / s
  3. C0.6 10^3 ~m / s
  4. D0.75 10^3 ~m / s

Correct answer

C. 0.6 10^3 ~m / s

Step-by-step solution

Phase velocity, v_p= k aligned & d v_p v_p = d - d k k & d k k = d - d v_p v_p =2 %-(-3 %)=5 % aligned Group velocity, v_g= d d k aligned & d d k =v_p ( d / d k / k )=1.5 10^3 ( 2 5 ) & =0.6 10^3 ~m / s aligned

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