Velocity, Period, and Transverse Wave

[Soaring Crane]

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.

 

[OlderDan]

The densities do not add. You need to find an expression for the time it takes for the wave to traverse each part of the string and add those to find the total time.