Past exam of the physics of the Earth as a Planet course of the University of Cambridge / 2013 / Paper 1 / 3 / a / Solution

For group velocity from a period-dependent phase velocity, start with $k=\omega /c_n(\omega )$ rather than equating group velocity to phase velocity. Differentiating,For the stated inverse-frequency term, $d{c}_n/d\omega =-a/{\omega }^2$, soThe inequality assumes positive frequency and physical positive phase velocity, with $a>0$. The symbol $a$ here has units of acceleration and is unrelated to the plate thickness in Question 1.