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A periodic function, also called a periodic waveform (or simply periodic wave), is a function that repeats its values at regular intervals or periods. The repeatable part of the function or waveform is called a cycle. [1] For example, the trigonometric functions, which repeat at intervals of radians, are
This is a list of some well-known periodic functions. The constant function f ( x ) = c , where c is independent of x , is periodic with any period, but lacks a fundamental period . A definition is given for some of the following functions, though each function may have many equivalent definitions.
Examples of phenomena resembling periodic travelling waves that have been found empirically include the following. Many natural populations undergo multi-year cycles of abundance. In some cases these population cycles are spatially organised into a periodic travelling wave.
Periodic waves oscillate repeatedly about an equilibrium (resting) value at some frequency. When the entire waveform moves in one direction, it is said to be a travelling wave; by contrast, a pair of superimposed periodic waves traveling in opposite directions makes a standing wave. In a standing wave, the amplitude of vibration has nulls at ...
Almost periodic function – Amplitude modulation – Amplitude – Beat – Chaos theory – Cyclic group – Diffraction – Doppler effect – Eigenstate – Eigenvalue – Fibonacci sequence – Fourier series – Frequency domain – Frequency spectrum – Hamiltonian (quantum mechanics) – Harmonic oscillator – Huygens–Fresnel ...
Simple examples of periodic waveforms include the following, where is time, is wavelength, is amplitude and is phase: . Sine wave: (,,,) = . The amplitude of the waveform follows a trigonometric sine function with respect to time.
Wavelength depends on the medium (for example, vacuum, air, or water) that a wave travels through. Examples of waves are sound waves, light, water waves and periodic electrical signals in a conductor. A sound wave is a variation in air pressure, while in light and other electromagnetic radiation the strength of the electric and the magnetic ...
Tracing the y component of a circle while going around the circle results in a sine wave (red). Tracing the x component results in a cosine wave (blue). Both waves are sinusoids of the same frequency but different phases. A sine wave, sinusoidal wave, or sinusoid (symbol: ∿) is a periodic wave whose waveform (shape) is the trigonometric sine ...