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Wave Propagation in a String of Varying Density

Consider a string of total length L, made up of three segments of equal length. The mass per unit length of the first segment is mu, that of the second is 2mu, and that of the third mu/4. The third segment is tied to a wall, and the string is stretched by a force of magnitude Ts applied to the first segment; Ts is much greater than the total weight of the string.

How long will it take a transverse wave to propagate from one end of the string to the other?
Express the time t in terms of L, mu, and Ts.

Solution Summary

This response calculates the time it will take for a transverse wave to move from one end of a piece of string to the other.