A circular loop of string rotates about its axis on a frictionless horizontal

Question:

A circular loop of string rotates about its axis on a frictionless horizontal plane at a uniform rate so that the tangential speed of any particle of the string is $\mathrm{U}$. If a small transverse disturbance is produced at a point of the loop, with what speed (relative to the string) will this disturbance travel on the string?

Solution:

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