Past exam of the mathematics course of the University of Cambridge / 2025 / ii / Paper 2 / 40A / a

Table of contents
- Solution a

Solution

Take the divergence of the elastic equation. With

θ = \nabla \cdot u

,

ρ θ_{tt} = (λ + 2 μ) \nabla^{2} θ .

Thus dilatational P-waves have speed

c_{P} = \frac{λ + 2 μ}{ρ} .

Taking the curl and writing

ω = \nabla \times u

eliminates the gradient term and gives

ρ ω_{tt} = μ \nabla^{2} ω .

Thus rotational S-waves have speed

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