Radio atmospheric km. For ELF waves (< 3 kHz), ray theory becomes invalid, and only mode theory is appropriate. Here, the zeroth mode begins to dominate and is responsible for the second window at greater distances. Resonant waves of this zeroth mode can be excited in the Earth–ionosphere waveguide cavity, mainly by the continuing current components of lightning flowing between two return strokes. Their wavelengths are integral fractions of the Earth's circumference, and their resonance frequencies can thus be approximately determined by "f" ≃ "mc"/(2π"a") ≃ 7.5 "m" Hz (with "m" = 1, 2, ...; "a" the Earth's radius and "c" the
Radio propagation propagation. The interference between the direct beam line-of-sight and the ground reflected beam often leads to an effective inverse-fourth-power (1/distance) law for ground-plane limited radiation. Lower frequency (between 30 and 3,000 kHz) vertically polarized radio waves can travel as surface waves following the contour of the Earth; this is called "groundwave" propagation. In this mode the radio wave propagates by interacting with the conductive surface of the Earth. The wave "clings" to the surface and thus follows the curvature of the Earth, so groundwaves can travel over mountains and beyond the horizon. Ground waves propagate in vertical polarization so vertical