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 the point $O$. A transverse wave pules (Pules 1) of wavelength ${\lambda }_0$ is produced at the point $O$ on the rope. The pulse takes time $T_{OA}$ to reach point $A$ If the wave pules of wavelength ${\lambda }_0$ is produced at point $A$ (Pules 2) without distributing the position of $M$ it takes time $T_{AO}$ to reached point $O$. Which of the following option is/are correct?

• A. The time $T_{AO}=T_{OA}$
• B. The velocity of the two pulses (Pules 1 and Pules 2) are the same at the midpoint of rope.
• C. The wavelength of Pules 1 becomes longer when it reaches point $A$.
• D. The velocity of any pules along the rope is independence of its frequency and wavelength.

Answer 1

Answer: (A)

The time $T_{AO}=T_{OA}$

At any point

$v=\sqrt{\frac{T}{\mu }}$ [$T\to$ Tension; $\mu \to$ mass per unit length]

So, velocity is independent of frequency and wavelength.

Also, therefore time from O to A and A to O will be the same.

$T_{OA}=T_{AO}$