 Home

Codex Wiki

List of universities

University of Cambridge

Course of the University of Cambridge

Mathematics course of the University of Cambridge

Past exam of the mathematics course of the University of Cambridge

2024

Paper 2

Taking the divergence of the elastic equation gives
$$
\rho\,\vartheta_{tt}=(\lambda+2\mu)\nabla^2\vartheta.
$$
Taking its curl gives
$$
\rho\,\Omega_{tt}=\mu\nabla^2\Omega.
$$
Thus the <Helmholtz separation of elastic waves> produces longitudinal P-waves and transverse S-waves with
$$
\boxed{c_p=\sqrt{\frac{\lambda+2\mu}{\rho}},
\qquad c_s=\sqrt{\frac{\mu}{\rho}}}.
$$

Solution

Past exam of the mathematics course of the University of Cambridge / 2024 / ii / Paper 2 / 40D / a / Solution

Past exam of the mathematics course of the University of Cambridge / 2024 / ii / Paper 2 / 40D / a / Solution

 Ancestors (11)

 Discussion (0)

 Articles by others on the same topic (0)

Past exam of the mathematics course of the University of Cambridge / 2024 / ii / Paper 2 / 40D / a / Solution

 Ancestors (11)

 Discussion (0)  Subscribe (1)

 Articles by others on the same topic (0)

 Discussion (0)