Sinusbølgen

Sinusbølgen, or the sine wave, is a smooth periodic oscillation that follows the sine function. It is one of the most fundamental waveforms in physics, engineering, and signal processing because many systems respond linearly to sinusoidal inputs and many signals can be represented as sums of sinusoids.

Mathematically, a sine wave can be written as y(t) = A sin(2π f t + φ), where A is the amplitude, f is the frequency, and φ is the phase. Equivalently, y(t) can be expressed using cosine or the angular frequency ω = 2π f as y(t) = A sin(ω t + φ). The wave is periodic with period T = 1/f and has a constant amplitude when ideal. The average value is zero over a full cycle, and the phase determines where in the cycle the wave begins.

Generation and use are widespread. In hardware, sine waves are produced by oscillators (LC, RC, crystal, or voltage-controlled oscillators) and by dedicated function generators. In software, digital oscillators generate samples at a specified sampling rate. Sine waves are essential in testing and analysis, serving as reference signals in measurement, audio, communications, and control systems.

Applications rely on the property that any linear system’s response to a sine wave can be described by amplitude scaling and phase shift. In analysis, sinusoidal components form the basis of Fourier analysis, allowing complex periodic signals to be decomposed into sums of sinusoids.