Serway & Jewett — Superposition and Standing Waves: Problem 8

Verify by direct substitution that the wave function for a standing wave given in Equation 17.1, \[y = (2A \sin kx) \cos \omega t\] is a solution of the general linear wave equation, Equation 16.27: \[\frac{\partial^2 y}{\partial x^2} = \frac{1}{v^2} \frac{\partial^2 y}{\partial t^2}\]