Asked by Waves - AEC

I have the following exercise:

Verify that Ex=f(z-ct)+g(z+ct) is a solution of the one dimensional wave equation.

But I don't get what I should do, I mean, isn't Ex the formula of the one dimensional wave equation itself? U.U

How can I verify it?

Thank you.
Answered by bobpursley
review section 5.2 of this: https://web.stanford.edu/class/math220a/handouts/waveequation1.pdf
Answered by Waves - AEC
Bobpursley coudl I get an email from you? I need to ask you something.
Answered by bobpursley
No emails. Our web safety issues don't allow that.
Answered by Waves - AEC
:( I could really use some assistance better than the provided from a input field of HTML xD, and my questions usually have symbols that require more precision in order for me to understand them.

Is there nothing we can do?
Answered by bobpursley
Not now, we are working on a more flexible input field. Or a white board.
Answered by Damon
The equation is:
d^2y/dx^2 = (1/c^2 )[d^2y/dt^2]

here:
d^2x/dz^2 = (1/c^2 )[d^2x/dt^2] with the strange letters for displacements
I will just do the half that is moving right (z+ct)= constant or f(z-ct)

write as f(w) where w = z-ct
df/dz = df/dw * dw/dz = df/dw
d^2f/dz^2 = d^2f/dw^2 dw/dz = d^2f/dw^2
and then
df/dt = df/dw * dw/dt = df/dw (-c) ah hah !
d^2f/dt^2 =d^2f/dw^2 (-c)(-c) = c^2 d^2f/dw^2

so in the end
d^2f/dt^2 /c^2 = d^2f/dw^2 = d^2f/dz^2
which is what we had to show.
note that due to the (-c)(-c) = c*c
it will come out the same for x+ct as for x-ct
There are no AI answers yet. The ability to request AI answers is coming soon!