Sine wave

"Sinusoid" redirects here. For the blood vessel, see Sinusoid (blood vessel).

The graphs of the sine and cosine functions are sinusoids of different phases.

The sine wave or sinusoid is a mathematical function that describes a smooth repetitive oscillation. It occurs often in pure mathematics, as well as physics, signal processing, electrical engineering and many other fields. Its most basic form as a function of time (t) is:

where:

• A, the amplitude, is the peak deviation of the function from its center position.
• ω, the angular frequency, specifies how many oscillations occur in a unit time interval, in radians per second
• φ, the phase, specifies where in its cycle the oscillation begins at t = 0.
  • When the phase is non-zero, the entire waveform appears to be shifted in time by the amount φ/ω seconds. A negative value represents a delay, and a positive value represents a "head-start".

	Sine wave 5 seconds of a 220 Hz sine wave
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The oscillation of an undamped spring-mass system around the equilibrium is a sine wave.

The sine wave is important in physics because it retains its waveshape when added to another sine wave of the same frequency and arbitrary phase. It is the only periodic waveform that has this property. This property leads to its importance in Fourier analysis and makes it acoustically unique.