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

Table of contents
- Solution a

Solution

Taking the divergence of the elastic equation gives

ρ ϑ_{tt} = (λ + 2 μ) \nabla^{2} ϑ .

Taking its curl gives

ρ Ω_{tt} = μ \nabla^{2} Ω.

Thus the Helmholtz separation of elastic waves produces longitudinal P-waves and transverse S-waves with

c_{p} = \frac{λ + 2 μ}{ρ}, c_{s} = \frac{μ}{ρ} .

 Ancestors (10)

 View article source

 Discussion (0)

There are no discussions about this article yet.

 Articles by others on the same topic (0)

There are currently no matching articles.

  See all articles in the same topic Create my own version