How Do You Simplify a Wave Equation in a Non-Uniform Pipe?

[andrey21]

Wave Equation (urgent)

Sounds waves in a pipe of varying cross-section are described by the wave equation

v² d/dx .(1/A.dAu/dx) = d²u /dt²

Where A = 0.2 +0.3x simplify the equation


My attempt at a solution

Sub in A:

v² d/dx ( 1/(0.2+0.3x) . d(0.2+0.3x)u/dx) =d²u/dt²

Not to sure where to go from here

 

[Wingeer]

Are you trying to solve the equation? If so, you should perhaps check out the method of separation of variables.

 

[andrey21]

No just simplify the equation then compare with general second order hyperbolic equation to find a,b,c, and e

 

[olivermsun]

I'm seeing some chain rule in your future...

 

[andrey21]

So by applying the chain rule this is my solution:

V² (1/0.2+0.3x) .(0.3u + (0.2+0.3x)du/dx)

Is this correct?