Question

A string of linear mass density $0.5gc{m}^{-1}$ and a total length $30cm$ is tied to a fixed wall at one end and to a frictionless ring at the other end. The ring can move on a vertical rod. A wave pulse is produced on the string which moves towards the ring at a speed of $20cm{s}^{-1}$. The pulse is symmetric about its maximum which is located at a distance of $20cm$ from the end joined to the ring. Assuming that the wave is reflected from the ends without loss of energy, find the time taken by the string to regain its shape.

• A. 2 sec
• B. 1sec
• C. 4 sec
• D. None of these

Answer 1

The correct option is A 2 sec

$\mu =0.5gc{m}^{-1}=0.5\times {10}^{-1}kg/m$

$l=30cm=0.3m$

$v+20cm{s}^{-1}=0.2m{s}^{-1}$

Since it's a free and end and not fixed one so the reflected wave will be in phase and be reflected as it is so the pulse will have to travel $40cm$

$v=20cm/s$

$\Rightarrow time=2sec$