Eduprobe
Question:
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?
The velocity of any pulse along the rope is independent of its frequency and wavelength
The velocities of the two pulses (Pulse 1 and Pulse 2) are the same at the midpoint of rope
The time TAO = TOA
The wavelength of Pulse 1 becomes longer when it reaches point A
Solution:
The correct options are A, B, and D.
A. As T and l are the same at the similar point, we have average velocity v = ∫v dt/dt = constant. Therefore, TAO = TOA.
B. At the midpoint, tension for both waves is the same, so the speed is the 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 = v/f ∝ 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.