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 `mu_2 = 4mu_1` and the third piece has mass per unit length `mu_3 = mu_1//4` .
(a) 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` .
(b) Does your answer to part (a) depend on the order in which the three piece are joined together? Explain.

Answer

A, B

Explanation

(a) `v_1 = sqrt (T//mu_1)`
` v_2 = sqrt (F//4mu_1) = 1/2 sqrt(F//mu_(1))`
`v_3 = sqrt (F//(mu_1//4)) = 2 sqrt(F//mu_1)`
` :. T = t_1 + t_2 + t_3 = L/ v_1 + L/v_2 + L/v_3`
= (7L)/2 sqrt (mu_1/F)` .