Electromagnetic Waves in Conducting Tubes

It is shown that the waves in a hollow conducting tube described by Carson and by Barrow may be represented as semi-standing waves due to the superposition of plane waves with normal phase velocity $\frac{c}{{\left(\kappa \mu \right)}^{\frac{1}{2}}}$ reflected back and forth from one side of the tube to the other. It is also shown that certain types of waves can be transmitted without attenuation in tubes of triangular, rectangular and hexagonal cross section.