Sine wave

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 $\cos{(x -\frac{\pi}{2})} = \sin{x}$ 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.