The Earth's resonant cavity refers to the Schumann resonances, which are global electromagnetic resonances in the Earth-ionosphere cavity. These resonances are caused by lightning discharges around the world and the space between the Earth's surface and the ionosphere acting as a waveguide.
The fundamental Schumann resonance mode occurs at approximately 7.83 Hz, but the Earth-ionosphere cavity supports multiple resonant modes with higher frequencies as well. The first few modes are typically referred to as follows:
- Fundamental mode: Approximately 7.83 Hz
- First harmonic: Approximately 14.1 Hz
- Second harmonic: Approximately 20.3 Hz
- Third harmonic: Approximately 26.4 Hz
It's important to note that these frequencies are approximate and can vary due to environmental conditions. Additionally, the amplitudes of the resonances can also vary depending on factors such as geographic location and time of day.
Mathematically, the resonant frequencies of the Earth-ionosphere cavity can be approximated using the following formula:
fₙ = (c / (2πR)) * sqrt(1 - (n / β)²)
Where: fₙ is the resonant frequency of the nth mode, c is the speed of light, R is the radius of the Earth, and β is a constant related to the speed of propagation of the electromagnetic waves in the waveguide.
In practice, determining the exact resonant frequencies of the Earth-ionosphere cavity can be challenging due to various factors affecting the ionosphere and the nature of the lightning discharges. Therefore, the values mentioned above are commonly used as approximations based on empirical observations.