Sinewave

A sine wave is a smooth, continuous periodic oscillation whose graph follows the sine function. It is considered a pure tone with a single frequency and no spectral harmonics, making it a fundamental building block in physics, engineering, and acoustics.

Mathematically, a sine wave in time is described by y(t) = A sin(2π f t + φ), where A is the amplitude, f the frequency, t time, and φ the phase. The angular frequency is ω = 2π f, and the period is T = 1/f. The waveform oscillates between −A and A.

In linear systems, sine waves are special because they retain their shape after passing through a linear time-invariant network; only amplitude and phase may change. A sine wave is also central to simple harmonic motion and to Fourier analysis, where any periodic signal can be expressed as a sum of sinusoids.

Generation and use: sine waves are produced by analog oscillators or digital function generators, and are ubiquitous in audio synthesis, communications, and measurement. In power systems, mains electricity is a sine wave. Real signals, however, may exhibit distortion, noise, and finite bandwidth, requiring filtering and proper sampling to avoid aliasing.