A block M hangs vertically at the bottom end of a uniform rope of constant mass per unit length. The top end…

A block M hangs vertically at the bottom end of a uniform rope of constant mass per unit length. The top end of the rope is attached to a fixed rigid support at O. A transverse wave pulse (Pulse 1) of wavelength λ0 is produced at point O on the rope. The pulse takes time TOA to reach point A. If the wave pulse of wavelength λ0 is produced at point A (Pulse 2) without disturbing the position of M it takes time TOA to reach point O. Which of the following options is/are correct?

  1. The velocity of any pulse along the rope is independent of its frequency and wavelength
  2. The velocities of two pulses are the same at the midpoint of rope
  3. The wavelength of pulse 1 becomes longer when it reaches point A
  4. The time TAO=TOA

Solution

(i)  Speed of wave is property of medium so time taken to cross the string will be equal

(ii)  Speeds are same but velocity is vector, has opposite directions

(iii)  Wavelength λ=vf=1fTμ and T0>TA

(iv)   Velocity of any pulse is v= Tμ and it is property of medium.

Asked in: JEE Advanced 2017 (Paper 1)

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