Homework Help: Electromagnetic Waves

1. Apr 6, 2005

pt176900

From Griffiths: Problem 9.4 Obtain Eq. 9.20 directly from the wave equation, by separation of variables.

Eq. 9.20: f(z,t)~ = integral [-inf, inf] A~(k)e^i(kz-wt) dk

where ~ denotes the complex conjugate

the wave equation: f''(z) = (1/v^2) f''(t)

I'm a little confused on how I can separate the variables. Can I assume that I can represent f(z,t) as A sin(kz)cos(kvt) and then calculate the aforementioned 2nd derivatives.

I think my reasoning is correct but my math.... well my math isn't up to par.

2. Apr 6, 2005

dextercioby

You want to solve the the 1D linear PDE

$$\frac{\partial^{2} f}{\partial z^{2}}=\frac{1}{v^{2}}\frac{\partial^{2} f}{\partial t^{2}}$$

with proper boundary conditions (field-type)...?

Use the Fourier transform...

Daniel.

3. Apr 8, 2005

pt176900

What are the boundary conditions for an electromagnetic wave?

4. Apr 8, 2005

dextercioby

There are none.Simply the solution be writible as a Fourier series (discrete spectrum of frequencies),or as Fourier integral...

Daniel.