A blcok M hangs vertically at the bottom end of uniform rope of constant mass per unit length. The top end of the rope is attached to 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?

The correct options are
A   The time TAO=TOA
B   The velocities of the two pulses (Pulse 1 and Pulse 2) are the same at the midpoint of rope
D   The velocity of any pulse along the rope is independent of its frequency and wavelength
    Speed of the wave is directly proportional to the tension T in the string and length l.
              Speed of the wave v=√Tμ
              where μ is mass of string per unit length.
A.    As T and l are same at the similar point 
            We have average velocity v=∫vdtdt=constant
             TAO=TOA
B.      At mid point, tension for both the waves is same, so speed is same. Hence B is correct.
C.      Speed is higher at the point where tension is larger i.e. at O.
        Since frequency is constant, wavelength of the wave λ=vν ⟹λ∝v
        Thus λ is longer at O.
         Hence C is incorrect.
D.    Velocity depends on tension, not frequency or wavelength. Hence D is also correct.