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## Homework Statement

Three pieces of string, each of length L, are joined together end-to-end, to make a combined string of length . The first piece of string has mass per unit length mu_1, the second piece has mass per unit length mu_1*4.00 , and the third piece has mass per unit length mu_1/4.00. If the combined string is under tension F, how much time does it take a transverse wave to travel the entire length 3L? Give your answer in terms of F, mu_1, and L.

## Homework Equations

v = sqrt(F/mu)

T = position/velocity = 3L/v ??

## The Attempt at a Solution

The answer is (7L/2)*sqrt(mu_1/F).

I understand the sqrt portion, but I am having difficulty with the multiplicative factor.

I thought the velocity would be:

v = sqrt(F/mu_total), where mu_total = mu_1 + 4*mu_1 + .25*mu_1 = 5.25*mu_1

T = 3L/sqrt(F/5.25*mu_1) = 3L*sqrt(5.25)*sqrt(mu_1/F)

How do I get the correct factor?

Thanks.