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JEE Advanced2017PhysicsWaves and SoundActual

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 λ 0 is produced at point O on the rope. The pulse takes time T O A to reach point A. If the wave pulse of wavelength λ 0 is produced at point A (Pulse 2) without disturbing the position of M it takes time T O

Options

  1. AThe velocity of any pulse along the rope is independent of its frequency and wavelength
  2. BThe velocities of two pulses are the same at the midpoint of rope
  3. CThe wavelength of pulse 1 becomes longer when it reaches point A
  4. DThe time T A O = T O A

Correct answer

A. The velocity of any pulse along the rope is independent of its frequency and wavelength

Step-by-step 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 = v f = 1 f T μ and T 0 > T A (iv) Velocity of any pulse is v = T μ and it is property of medium.

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