Why is the amplitude of wave guide indepentent of z?

[Ethan0718]

Griffiths p406

it talks about Guided waves

9.5.1
we consider electromagnetic waves confined to te interior of a hollow pipe, or wave quide.
We'll assume the wave guide is a perfect conductor, so that E=0 and B=0 inside the material itself,
and hence the boundary conditions at the inner wall are
E^|| = 0
B ( it's perpendicular to surface of conductor ) = 0

http://img593.imageshack.us/i/imageyyf.jpg/

please see this photo...

Hmm...Why are both of "E₀、B₀ independent of z?

Is it about the fact that it propagate down the tube along z axis?

 

[olivermsun]

Short answer: Because it's a "wave guide." :)

(As you note, it comes from the requirement that the waves propagate down the channel. The boundary conditions place strict requirements on the wave solutions which survive and propagate, i.e., they must interfere constructively)