Halliday, Resnick & Walker — Waves–I: Problem Problem_50

For a particular transverse standing wave on a long string, one of the antinodes is at \(x = 0\) and an adjacent node is at \(x = 0.10 \text{ m}\). The displacement \(y(t)\) of the string particle at \(x = 0\) is shown in Fig. 16.17, where the scale of the \(y\) axis is set by \(y_s = 4.0 \text{ cm}\). When \(t = 0.50 \text{ s}\), what is the displacement of the string particle at (a) \(x = 0.20 \text{ m}\) and (b) \(x = 0.30 \text{ m}\)? What is the transverse velocity of the string particle at \(x = 0.20 \text{ m}\) at (c) \(t = 0.50 \text{ s}\) and (d) \(t = 1.0 \text{ s}\)? (e) Sketch the standing wave at \(t = 0.50 \text{ s}\) for the range \(x = 0\) to \(x = 0.40 \text{ m}\).