Wave Equation in 1-d Proof/Verify

[hitman0097]

Homework Statement

Verify that Acos(kx-ωt) and Bsin(kx-ωt) are solutions of the one dimensional wave eqn. if v=ω/k. Does f(x,t)=(ax+bt+c)^2 represent a propagating wave? If yes what is its velocity?

Homework Equations

I know the partial differ. eqns. for the wave equation are
d^2 U/dz^2 = 1/c^2 d^2E/dt^2 for the function f(x-ct) + g(x+ct)
The lapacians for E is μ_oε_o d²E/dt²

The Attempt at a Solution

I am just confused as to how to show this? And same for part b.). To verify something would I have to just take any value for v and show it for the first part. (I'll be talking to my prof. about this problem today as well) Thanks any help and hints are appreciated.

 

[BruceW]

I know the partial differ. eqns. for the wave equation are
d^2 U/dz^2 = 1/c^2 d^2E/dt^2 for the function f(x-ct) + g(x+ct)
The lapacians for E is μ_oε_o d²E/dt²

I don't really get what you mean here. Usually, the wave equation is just:
$$\frac{\partial^2 U}{\partial z^2} = \frac{1}{c^2} \frac{\partial^2 U}{\partial t^2}$$
And for the question, they've given you some possible solutions. Its fairly simple to show that they satisfy the wave equation. Think about it - if you just thought you had worked out a solution, then how would you check that it is correct?

 

[hitman0097]

Yeah, I think I was just making the problem harder than it was. I understand it better now I think about it. Thanks!