As shown in ATTACHMENT #1, a wave is traveling toward +x on a wire. The motion of a point at x1= .45 m is shown. From the diagram, initial value of y is .12 meters and is increasing so initial slope is positive. The amplitude is .20 m, and the period is .5 sec.
From this information, develop the equation y(x,t) of the wave, then find and show the first three time coordinates on the time axis.
From the graph of a traveling wave on a wire, at x1 known, obtain information required to write the wave equation y(x,t), and find the time intercepts.
Known information is that at t=0, yo= .12 m, and slope is positive. Also, T= .5 sec therefore we have angular frequency w = (2 Pi)/T or w= 4 Pi rad/sec.
The general equation form of a traveling wave: y=ym sin (kx - wt). gives here:
(1) y= .2 sin (kx - 4 Pi t) in which k is the propagation constant.
In a step by step process, the problem is solved.