An unwanted frequency component that is an integer multiple of the fundamental operating frequency.Harmonics are frequency components that appear at integer multiples of a system's fundamental operating frequency. If a device operates at 60 Hz, its harmonics appear at 120 Hz, 180 Hz, 240 Hz, and so on. They are ubiquitous in physics and engineering, arising whenever a system behaves nonlinearly — that is, when its response is not strictly proportional to the input. In power systems, harmonics distort the ideal sinusoidal voltage and current, causing inefficiencies and overheating. In optics, harmonics are generated when intense light passes through certain crystals, producing new colors at multiples of the original frequency.
The concept of harmonics in vibrating strings was known to Pythagoras in ancient Greece, but the mathematical treatment of harmonics as integer multiples of a fundamental frequency was formalized by Joseph Fourier in the early 19th century.
Harmonics emerge from nonlinearity. A linear system, like a simple pendulum at small angles, responds at exactly the driving frequency. But when the response becomes nonlinear — for example, a spring that stiffens as it stretches, or an electronic amplifier that clips peaks — the output contains components at multiples of the input frequency. Mathematically, this is described by a Fourier series: any periodic, distorted waveform can be decomposed into a sum of sine waves at the fundamental frequency and its integer multiples. The relative amplitudes of these harmonics determine the shape of the distorted wave.
Harmonics are exploited in laser physics to generate new wavelengths: a crystal like potassium titanyl phosphate doubles the frequency of an infrared laser to produce green light, a technique used in laser pointers and scientific instruments.
In power grids, the third harmonic (150 Hz in Europe, 180 Hz in the US) is particularly problematic because it adds up in the neutral wire of three-phase systems, potentially causing overheating even when each phase is balanced.





