Two wires of different linear mass densities are soldered together end to end and are then stretched under a tension F (the tension is the same in both wires). The wave speed in the second wire is three times that in the first wire. When a harmonic wave traveling in the first wire is reflected at the junction of the wires, the reflected wave has half the amplitude of the incident wave.

(a) If the amplitude of the incident wave is A, what are the amplitudes of the reflected and transmitted waves?

(b) Assuming no loss in the wire, what fraction of the incident power is reflected at the junction and what fraction is transmitted?

(c) Show that the displacement just to the left of the junction equals that just to the right of the junction.