AC frequency

AC frequency f is the number of complete sinusoidal cycles per second of an alternating current or voltage, measured in hertz (Hz). The angular frequency ω = 2πf is the more common symbol in analytical work, because ω appears directly in the exponentials e^(jωt) of phasor analysis and the impedances jωL and 1/(jωC) of reactive elements.

Two standard grid frequencies divide the world: 50 Hz in Europe, Asia outside Japan, Africa, Australia, and most of South America; 60 Hz in North America, parts of South America, and Japan (with a complicated 50/60 Hz split across the country). The difference has historical rather than physical origins: German and American engineers independently chose different defaults in the 1890s. Both are compatible with all standard electrical design; the only visible differences are slightly smaller/lighter transformers at 60 Hz (ferromagnetic cores work a bit more efficiently at higher frequency), and a 50/60 Hz flicker at the stroboscopic edges of fluorescent lighting.

Above power frequencies, AC extends across an enormous range. Audio: 20 Hz – 20 kHz. Ultrasonic: 20 kHz – 1 MHz (sonar, NDT, medical imaging). Radio: 100 kHz (LW) to 30 GHz (microwave) — every broadcast band, cellular, Wi-Fi, satellite, radar. Visible light: 4 × 10¹⁴ – 8 × 10¹⁴ Hz. X-rays: 10¹⁶ – 10¹⁹ Hz. Gamma rays: above 10¹⁹ Hz. At each frequency scale, the wavelength (c/f) determines whether circuit-theory (f low, wavelength large) or field-theory (f high, wavelength comparable to or smaller than circuit dimensions) is the appropriate framework. The boundary is around 100 MHz for most consumer hardware and around 1 GHz for precision instrumentation.