Sine wave

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An ideal sine wave is a waveform whose graph is identical to the generalized sine function y = Asin[ω(x − α)] + C, where A is the amplitude, ω is the angular frequency (2π/P where P is the wavelength), α is the phase shift, and C is the vertical offset.

The graph of cos(x) is also a sine wave, since <math>\cos{(x -\frac{\pi}{2})} = \sin{x}<math> Sine waves (of the general form) are characterized by being the only functions with a single "pure" frequency; this is used in Fourier analysis.

Sine waves often generate mellower and generally softer tones than sawtooth waves or square waves.

See also:

• Fourier transform
• Harmonic series