How long does it take this transverse wave to travel along a string

[jcadams9]

Homework Statement

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 L, F, and mu_1.

Three pieces of string, each of length L, are joined together end-to-end, to make a combined string of length 3L. The first piece of string has mass per unit length mu_1, the second piece has mass per unit length 4mu _1, and the third piece has mass per unit length (1/4)mu_1

Homework Equations

V= (Sqrt (Tension/Linear Mass Density)

V/L=T

The Attempt at a Solution

Well it seems like I could find the speed of the wave over each section of the string, average all three to get the average velocity and simply divide by the total length of the string 3L like so but this is giving me an incorrect answer.

((Sqrt(F/mu_1) + Sqrt(4F/mu_1) +Sqrt(F/4mu_1)) /3) / (3*L)

 

[G01]

Try finding the time for the wave to travel through each string and add all three up.

Is the answer different?

 

[jcadams9]

Actually it is different - I'll give that a try thanks =)