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Q.

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 wave pulse of wavelength λ0 is produced at point A (Pulse 2) without disturbing  the position of M it takes time TAO to reach point  O. Which of the following options is/are correct?

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a

The time  TAO=TOA

b

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

c

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

d

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

answer is A.

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Detailed Solution

Velocity of the wave depends upon the tension in the rope and mass per unit length of the rope. v=Tμ velocity is independent of frequency and wavelength.Since tension at the point is same  , therefore speed at the point will also be same.The direction of the motion of pulses is opposite, so velocities will be equal and opposite.The velocities at any position depends only on tension at that point (μ=constant)therefore time taken for the wave the reach A from O and O from A will be same.Also, λ=vf=1fTμTension decreases as we move from O to A , therefore λ becomes shorter from O to A.
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