In the region of centimeter wave, metallic hollow pipes are widely used as transmission apparatus and metallic cavities are used as resonators. Many mathematical investigations regarding electromagnetic waves in hollow pipes and cavities have been made since the year 1936. Some effective methods, however, are not hitherto put to use. In this paper the following problems are treated: (1) the applications of variation principle to proper oscillations of cavities and pipes, (2) the general, formulation for radiation field of a dipole in a pipe, (3) quasi-static approximation and its application to iris-diaphragms, (4) applications of W. K. B. method to pipes with non-uniform cross section and problem of tunnel-effect, (5) application of the perturbation method to curving pipes.
Gauss’ system of units is used.
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