Why does wave length increase when waves entering a waveguide?
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Waves in open space propagate in all directions, as spherical waves. In this way they lose their power proportionally to the square of the distance; that is, at a distance R from the source, the power is the source power divided by R2. The waveguide confines the wave to propagation in one dimension, so that (under ideal conditions) the wave loses no power while propagating.

Waves are confined inside the waveguide due to total reflection from the waveguide wall, so that the propagation inside the waveguide can be described approximately as a "zigzag" between the walls. This description is exact for electromagnetic waves in a hollow metal tube with a rectangular or circular cross section.

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