Chapter 13.10, Problem 25MP

The Klein-Gordon equation is ${\nabla }^{2}u=\left(1/v^2\right){\partial }^{2}u/\partial t^2+{\lambda }^{2}u.$ This equation is of interest in quantum mechanics, but it also has a simpler application. It describes, for example, the vibration of a stretched string which is embedded in an elastic medium. Separate the one-dimensional Klein-Gordon equation and find the characteristic frequencies of such a string.