Serway & Jewett — Wave Motion: Problem 23

A sinusoidal sound wave moves through a medium and is described by the displacement wave function \[s(x, t) = 2.00 \cos (15.7x - 858t)\] where \(s\) is in micrometers, \(x\) is in meters, and \(t\) is in seconds. Find (a) the amplitude, (b) the wavelength, and (c) the speed of this wave. (d) Determine the instantaneous displacement from equilibrium of the elements of the medium at the position \(x = 0.0500 \text{ m}\) at \(t = 3.00 \text{ ms}\). (e) Determine the maximum speed of the element’s oscillatory motion.