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A block M hangs vertically at the bottom end A of a uniform rope of constant mass per unit length. The top end of the rope is attached to a fixed rigid support at 0. 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 $T_{AO}$ to reach point O. Which of the following options is/are correct?

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The velocities of the two pulses (Pulse 1 and Pulse 2) are the same at the midpoint of rope

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

The wavelength of Pulse 1 becomes longer when it reaches point A

The time $T_{AO} = T_{OA}$

answer is A, B, D.

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Detailed Solution

$V = \sqrt{\frac{T}{μ}},$ so speed at any position will be same for both pulses, therefore time taken by both pulses will be same.

$λ f = v \Rightarrow λ = \frac{V}{f} \Rightarrow λ \propto V$ , since when pulse 1 reaches

end A, speed decreases therefore $λ$ decreases.

Therefore options (1),(2) and (4) are correct ..

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