Halliday, Resnick & Walker — Waves-I: Problem 38

38 Figure 16-33 shows the transverse velocity \(u\) versus time \(t\) of the point on a string at \(x = 0\), as a wave passes through it. The scale on the vertical axis is set by \(u_s = 12 \text{ m/s}\). The wave has the generic form \(y(x, t) = y_m \sin(kx - \omega t + \phi)\). What then is \(\phi\)? (Caution: A calculator does not always give the proper inverse trig function, so check your answer by substituting it and an assumed value of \(\omega\) into \(y(x, t)\) and then plotting the function.)