Halliday, Resnick & Walker — Waves–I: Problem Problem_11

A sinusoidal transverse wave of wavelength 20 cm travels along a string in the positive direction of an \(x\) axis. The displacement \(y\) of the string particle at \(x = 0\) is given in Fig. 16.11 as a function of time \(t\). The scale of the vertical axis is set by \(y_s = 4.0 \text{ cm}\). The wave equation is to be in the form \(y(x, t) = y_m \sin(kx \pm \omega t + \phi)\). (a) At \(t = 0\), is a plot of \(y\) versus \(x\) in the shape of a positive sine function or a negative sine function? What are (b) \(y_m\), (c) \(k\), (d) \(\omega\), (e) \(\phi\), (f) the sign in front of \(\omega\), and (g) the speed of the wave? (h) What is the transverse velocity of the particle at \(x = 0\) when \(t = 5.0 \text{ s}\)?