JEE Advanced 2017 · Paper 1 · Physics Q3

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PhysicsMultiple correct+4 / -2Question 3 of 54

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 $\lambda_0$ is produced at point $O$ on the rope. The pulse takes time $T_{OA}$ to reach point $A$ . If the wave pulse of wavelength $\lambda_0$ 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?

A uniform rope hangs from a rigid support at O, with block M attached at its lower end A. Pulse 1 starts at O travelling down; Pulse 2 starts at A travelling up.

The time

T_{AO} = T_{OA}

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

The wavelength of Pulse 1 becomes longer when it reaches point

A

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

Answer and worked solution

Official answer: A, D

Speed. At height $y$ above $A$ the tension is $T(y)=Mg+\mu gy$ , so the speed $v=\sqrt{T/\mu}$ depends only on position.

(A) The travel time $\displaystyle\int_0^L\frac{dy}{v(y)}$ is the same whichever way the pulse goes. True.
(B) At the midpoint both pulses have the same speed but move in opposite directions, so their velocities differ. False.
(C) The frequency stays fixed, and near $A$ the tension and speed are smaller. So the wavelength $\lambda=v/f$ becomes shorter. False.
(D) $v=\sqrt{T/\mu}$ involves neither frequency nor wavelength (no dispersion). True.

(A), (D)

Topics:Speed of waves Free body diagrams

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JEE Advanced 2017 · Paper 1, Physics question 3