Serway & Jewett — Superposition and Standing Waves: Problem 10

A standing wave is described by the wave function \[ y = 6 \sin \left( \frac{\pi}{2} x \right) \cos(100\pi t) \] where \( x \) and \( y \) are in meters and \( t \) is in seconds. (a) Prepare graphs showing \( y \) as a function of \( x \) for five instants: \( t = 0 \), \( 5 \text{ ms} \), \( 10 \text{ ms} \), \( 15 \text{ ms} \), and \( 20 \text{ ms} \). (b) From the graph, identify the wavelength of the wave and explain how to do so. (c) From the graph, identify the frequency of the wave and explain how to do so. (d) From the equation, directly identify the wavelength of the wave and explain how to do so. (e) From the equation, directly identify the frequency and explain how to do so.