Chapter 18, Problem 18.16P

Verify by direct substitution that the wave function for a standing wave given in Equation 17.1,

$y=(2A\sin kx)\cos wt$

is a solution of the general linear wave equation, Equation 16.27:

$\frac{{\partial }^{2}y}{\partial x^2}=\frac{1}{v^2}\frac{{\partial }^{2}y}{\partial t^2}$