A string of linear mass density 0.5 g/cm and a total length 30 cm


A string of linear mass density $0.5 \mathrm{~g} / \mathrm{cm}$ and a total length $30 \mathrm{~cm}$ 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 $20 \mathrm{~cm} / \mathrm{s}$. The pulse is symmetric about its maximum which is located at a distance of $20 \mathrm{~cm}$ from the end joined to the ring.

a. Assuming that the wave is reflected from the ends without loss of energy, find the time taken by the string to regain its shape.

b. The shape of the string changes periodically with time. Find this time period.

c. What is the tension in the string?


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