The relationship between wavelength and the Earth's circumference

The key to understanding the Schumann resonance is the relationship between wavelength and the Earth's circumference. Resonance occurs when the wavelength "fits" around the entire planet in an integer manner.

We calculate the wavelength from the fundamental relation \lambda = c / f, where c \approx 3 \times 10^8 m/s is the speed of light and f is the frequency. For the fundamental mode \lambda = 3 \times 10^8 / 7{,}83 \approx 38\,000 km. This is remarkably close to the circumference of the Earth, which is approximately 40,000 km. The wavelength of the first mode is therefore roughly equal to the circumference of the planet — and that is precisely why resonance arises at this frequency: the wave, after circling the Earth, returns in phase with itself.

Higher modes correspond to cases where twice, three times, etc. the basic pattern "fits" around the Earth's circumference, which corresponds to the higher frequencies of the series 14.3; 20.8; 27.3; 33.8 Hz (see #4). This simple geometric relationship between the size of the planet and the wavelength is the core of Schumann's original prediction Schumann 1952 and is commonly given in reviews Price 2016Sentman 1995. The real values are moreover modified by losses in the ionosphere (see #4 and cluster C).