Schumann's Note

Plate 94 speaks for itself: “Lightning rings the planet at 7.8 hertz.”

The Physics

The ground and the ionosphere form a spherical cavity. Lightning excites its resonances, the lowest near 7.8 Hz, a wave whose wavelength is about Earth's circumference.

f_n = (c / 2πR) √(n(n + 1))

• f_n: ideal mode frequency, Hz
• c: speed of light, m s⁻¹
• R: Earth radius 6.371×10⁶ m
• n: mode number, integer

The ideal lossless cavity gives f₁ ≈ 10.6 Hz. Observed modes are ≈ 7.8, 14.3 and 20.8 Hz.

Honest caveat: Losses in the ionosphere pull the observed frequencies below the ideal formula.

Sources

• W. O. Schumann, Z. Naturforsch. A 7, 149 (1952).
• M. Balser, C. A. Wagner, Nature 188, 638 (1960).

On the poster

Plate 094, “Schumann's Note”: the pixel-art plate with its slogan “Lightning rings the planet at 7.8 hertz.”, the key equation and the facts panel shown above. Pixelated Physics. Physics. Personified.