(3) Imagine a string that is fixed at both ends (e.g. a guitar string). When plucked, the string forms a standing wave of varying amplitude. The vertical displacement u of the string varies with position r and time t and is given by u(x, t) = 2sin(nx) sin (#) , for 0 0. (a) Traces: (i) Show that if we freeze time, the string will form a sine curve. (ii) Show that if we focus on a single point on the string, we will see it oscillate up and down. (b) Give the period of the motion in time. Hint: find the period of sin (#)