A block M hangs vertically at the bottom end of a uniform rope of cons

1.	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 the 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?(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. (C) The wavelength of Pulse 1 becomes longer when it reaches point A. (D) The velocity of any pulse along the rope is independent of its frequency and wavelength.
Answer» (A) The time T_AO = T_OA (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 transverse pulse at the point = \(\sqrt{\frac{Tension in ropeat the point}{Linear mass density of rope}}\) So, T_AO = T_OA Wavelength becomes longer when speed of the pulse increases.

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 the 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?(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. (C) The wavelength of Pulse 1 becomes longer when it reaches point A. (D) The velocity of any pulse along the rope is independent of its frequency and wavelength.

Answer»

(A) The time T_AO = T_OA

(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 transverse pulse at the point = \(\sqrt{\frac{Tension in ropeat the point}{Linear mass density of rope}}\)