A harmonic wave is travelling on string 1. At a junction with string 2 it is partly reflected and partly transmitted. The linear mass density of the second string is four times that of the first string, and that the boundary between the two strings is at x=0. If the expression for the incident wave is
`y_i = A_i cos (k_1 x-omega_1t)`
(a) What are the expressions for the transmitted and the reflected waves in terms of `A_i, k_1` and `omega_1`?
(b) Show that the average power carried by the incident wave is equal to the sum of the average power carried by the transmitted and reflected waves.

Options

A. `1/3 A_i cos (2k_1x-omega_1t)`
B. `3/2 A_i cos (2k_1x-omega_1t)`
C. `2/3 A_i cos (2k_1x-omega_1t)`
D. None

Answer

C