Halliday, Resnick & Walker — Waves–I: Problem Problem_70

Figure 16.23 shows transverse acceleration \(a_y\) versus \(t\) of the point on a string at \(x = 0\), as a wave in the form of \(y(x, t) = y_m \sin(kx - \omega t + \phi)\) passes through that point. The scale of the vertical axis is set by \(a_s = 400 \text{ m/s}^2\). 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.)