Radio propagation antennas (monopoles) are required. Since the ground is not a perfect electrical conductor, ground waves are attenuated as they follow the Earth’s surface. Attenuation is proportional to frequency, so ground waves are the main mode of propagation at lower frequencies, in the MF, LF and VLF bands. Ground waves are used by radio broadcasting stations in the MF and LF bands, and for time signals and radio navigation systems. At even lower frequencies, in the VLF to ELF bands, an Earth-ionosphere waveguide mechanism allows even longer range transmission. These frequencies are used for secure military communications. They can also penetrate
Atmospheric tide The latitudinal structure of the tides is described by the "horizontal structure equation" which is also called "Laplace's tidal equation": with "Laplace operator" using formula_30, formula_31 and "eigenvalue" Hence, atmospheric tides are eigenoscillations (eigenmodes)of Earth's atmosphere with eigenfunctions formula_33, called Hough functions, and eigenvalues formula_34. The latter define the "equivalent depth" formula_35 which couples the latitudinal structure of the tides with their vertical structure. Longuet-Higgins has completely solved Laplace's equations and has discovered tidal modes with negative eigenvalues ε (Figure 2). There exist two kinds of waves: class 1 waves, (sometimes called gravity waves), labelled by positive n, and class