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.
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?