Halliday, Resnick & Walker — Waves–I: Problem Problem_91

In a demonstration, a \(1.2\text{ kg}\) horizontal rope is fixed in place at its two ends (\(x = 0\) and \(x = 2.0\text{ m}\)) and made to oscillate up and down in the fundamental mode, at frequency \(5.0\text{ Hz}\). At \(t = 0\), the point at \(x = 1.0\text{ m}\) has zero displacement and is moving upward in the positive direction of a \(y\) axis with a transverse velocity of \(5.0\text{ m/s}\). What are (a) the amplitude of the motion of that point and (b) the tension in the rope? (c) Write the standing wave equation for the fundamental mode.