Waves on stretched string: Wave velocity and time taken.

(See attached file for full problem description with symbols and diagrams)
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Consider a string of total length , made up of three segments of equal length. The mass per unit length of the first segment is , that of the second is , and that of the third . The third segment is tied to a wall, and the string is stretched by a force of magnitude applied to the first segment; is much greater than the total weight of the string.
Part A
How long will it take a transverse wave to propagate from one end of the string to the other?
Express the time in terms of , , and Ts.

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