Serway & Jewett — Wave Motion: Problem 8

A sinusoidal wave traveling in the negative \(x\) direction (to the left) has an amplitude of \(20.0 \text{ cm}\), a wavelength of \(35.0 \text{ cm}\), and a frequency of \(12.0 \text{ Hz}\). The transverse position of an element of the medium at \(t = 0\), \(x = 0\) is \(y = -3.00 \text{ cm}\), and the element has a positive velocity here. We wish to find an expression for the wave function describing this wave. (a) Sketch the wave at \(t = 0\). (b) Find the angular wave number \(k\) from the wavelength. (c) Find the period \(T\) from the frequency. Find (d) the angular frequency \(\omega\) and (e) the wave speed \(v\). (f) From the information about \(t = 0\), find the phase constant \(\phi\). (g) Write an expression for the wave function \(y(x, t)\).