Past exam of the mathematics course of the University of Cambridge / 2022 / ii / Paper 1 / 40C / a

Table of contents
- Solution a

Solution

Write

ρ = ρ_{0} + ρ

,

p = p_{0} + p

, and let

u

be small. Linearized mass and momentum conservation are

\partial_{t} ρ + ρ_{0} \nabla \cdot u = 0, ρ_{0} \partial_{t} u = - \nabla p .

The linearized equation of state is

p = c_{0}^{2} ρ

. Differentiate the first equation in time and eliminate the velocity with the second to obtain the wave equation

\partial_{t}^{2} p - c_{0}^{2} \nabla^{2} p = 0 .

 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