Past exam of the mathematics course of the University of Cambridge / 2005 / iii / Paper 82 / 2 / Solution

Take a stable isotropic elastic material with mass density $\rho >0$ and Lamé parameters $\lambda ,\mu$, where $\mu >0$ and $3\lambda +2\mu >0$. Its elastic stiffness tensor isThe P wave is longitudinal and the S wave transverse. The wavefront-transport alternative and all three steps of the Love wave alternative are given below.