Ideal vs. real lossy cavity — the frequency shift

The key difference between theory and measurement lies in the losses. The ideal cavity (perfect conductors) gives modes ≈ 10.6; 18.4; 26.0; 33.5; 41.1 Hz. The real cavity has an ionosphere with finite, height-varying conductivity, so electromagnetic energy partially penetrates into the upper boundary and is lost there. These losses effectively "enlarge" the cavity and lower the resonance frequencies by approximately 20-25 %.

The result is observed frequencies of approximately 7.83; 14.3; 20.8; 27.3; 33.8 Hz for the first five modes Sentman 1995Nickolaenko Hayakawa 2002. The shift from the ideal to reality is therefore substantial — it is not a second-order correction but a dominant effect that distinguishes the real planetary resonance from the textbook calculation.

Physically the shift is described by introducing a complex wave constant: both the frequency and the attenuation follow from a complex solution, in which the real part determines the position of the line and the imaginary part its width (see #19, #23). The specific values moreover fluctuate with the time of day, solar activity and the state of the ionosphere.