Halliday, Resnick & Walker — Waves–I: Problem Problem_66

Figure 16.21 shows the displacement \(y\) versus time \(t\) of the point on a string at \(x = 0\), as a wave passes through that point. The scale of the \(y\) axis is set by \(y_s = 6.0 \text{ mm}\). The wave is given by \(y(x, t) = y_m \sin(kx - \omega t + \phi)\). What 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.)