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 `lamda_(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 `lamda_(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?

Options

A. The velocities of the two pulses (Pulse 1 and Pulse 2) are the same at the midpoint of rope
B. The velocity of any pulse along the rope is independent of its frequency and wavelength
C. The wavelength of Pulse 1 becomes longer when it reaches point A
D. The time `T_(AO)=T_(OA)`

Answer

B, D

Explanation

Velocity of the wave depends upon the trnsion in the rope and mass per unit length of the rope. `implies` velocity is dependent of frequency and wavelength
option (B) is correct
since tension at the point is same .therefore speed at the point will also be same.Option(A) is correct since the dirsction of the motion of pilses is opposite .,velocitis will be equal and opposite.with this point of view A will be incorrect since the velocities at position dependent only on tension at every point `(mu="constant") `therefore time taken for the wave the reach A from O and O from A will be same.
`T_(OA)=T_(AO)`
Option (D) is correct
`v=lambdav`
since v depends on source
`implies lambda prop v implies lambda prop sqrtT`
Tension decreases as we move from O to A ,therefore `lambda` becomes shorte. Option (C) is icorrect.