harmonics

Harmonics are sinusoidal components of a periodic waveform whose frequencies are integer multiples of a fundamental frequency. In Fourier analysis, any periodic signal can be decomposed into a sum of harmonics.

The fundamental is the first harmonic; the second harmonic has frequency twice the fundamental; the third triple, etc. Amplitudes vary with the source and shape the timbre. In ideal simple harmonic motion only the fundamental exists.

In acoustics and music, the harmonic series arises from resonances of strings and air columns. For a vibrating string, the spectrum includes integer multiples; real strings produce a spectrum with amplitudes shaped by stiffness and boundary conditions. Wind instruments also produce overtones depending on bore shape. The perceived pitch is determined by the fundamental, while higher harmonics contribute to timbre.

In electrical engineering, non-linear loads distort waveforms, generating harmonics that can affect power systems. Harmonic distortion is quantified by total harmonic distortion (THD) and can be mitigated with filters, passive or active, and by designing equipment to minimize nonlinearity.

In signal processing, harmonics are used in sound synthesis, and Fourier transforms enable spectral analysis. The term "harmonics" is also used in optics and other wave phenomena.