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Encyclopedia > Sine wave
The oscillation of an undamped spring-mass system around the equilibrium is a sine wave.
The oscillation of an undamped spring-mass system around the equilibrium is a sine wave.

The sine wave or sinusoid is a function that occurs often in mathematics, physics, signal processing, electrical engineering, and many other fields. Its most basic form is: A sinusoid is a small blood vessel similar to a capillary but with a fenestrated endothelium. ... A Plot I made with Gnuplot and manually improved the labeling on. ... A Plot I made with Gnuplot and manually improved the labeling on. ... Image File history File links No higher resolution available. ... Euclid, Greek mathematician, 3rd century BC, as imagined by by Raphael in this detail from The School of Athens. ... This is a discussion of a present category of science. ... Signal processing is the processing, amplification and interpretation of signals, and deals with the analysis and manipulation of signals. ... Electrical Engineers design power systems… … and complex electronic circuits. ...

y = A cdot sin(omega t + theta)

which describes a wavelike function of time (t) with:

  • peak deviation from center  = A (aka amplitude)
  • angular frequency omega, (radians per second)
  • phase or phase shift = θ
    • When the phase is non-zero, the entire waveform appears to be shifted in time by the amount θ/ω seconds. A negative value represents a delay, and a positive value represents a "head-start".

Contents

It has been suggested that this article or section be merged into Angular velocity. ... Some common angles, measured in radians. ... This article is about a portion of a periodic process. ... This article is about a portion of a periodic process. ...

General form

In general, the function may also have:

  • a spatial dimension, x (aka position), with frequency k (also called wave number)
  • a non-zero center amplitude, D (also called DC offset)

which looks like this: Wavenumber in most physical sciences is a wave property inversely related to wavelength, having SI units of reciprocal meters (m−1). ... Direct current (DC or continuous current) is the continuous flow of electricity through a conductor such as a wire from high to low potential. ...

 y = Acdot sin(omega t - kx + theta) + D.,

The wave number is related to the angular frequency by:.

 k = { omega over c } = { 2 pi f over c } = { 2 pi over lambda }

where λ is the wavelength, f is the frequency, and c is the speed of propagation. The wavelength is the distance between repeating units of a wave pattern. ... FreQuency is a music video game developed by Harmonix and published by SCEI. It was released in November 2001. ... The phase velocity of a wave is the rate at which the phase of the wave propagates in space. ...


This equation gives a sine wave for a single dimension, thus the generalized equation given above gives the amplitude of the wave at a position x at time t along a single line. This could, for example, be considered the value of a wave along a wire.


A two-dimensional example would describe the amplitude of a two-dimensional wave at a position (xy) at time t. This could, for example, be considered the value of a water wave in a pond after a stone has been dropped in. Although this example is really a three dimensional wave it demonstrates the point; a more accurate example would be the propagation of an electrical wave through a conducting plane.


Occurrences

This wave pattern occurs often in nature, including ocean waves, sound waves, and light waves. Also, a rough sinusoidal pattern can be seen in plotting average daily temperatures for each day of the year, although the graph may resemble an inverted cosine wave. A wave is a disturbance that propagates through space or spacetime, transferring energy and momentum and sometimes angular momentum. ... The Ocean Waves, see I Can Hear the Sea Ocean waves Ocean surface waves are surface waves that occur in the upper layer of the ocean. ... Sound is a disturbance of mechanical energy that propagates through matter as a wave. ... This article does not cite any references or sources. ... In mathematics, the trigonometric functions are functions of an angle, important when studying triangles and modeling periodic phenomena. ...


Graphing the voltage of an alternating current gives a sine wave pattern. In fact, graphing the voltage of direct current full-wave rectification system gives an absolute value sine wave pattern, where the wave stays on the positive side of the x-axis. City lights viewed in a motion blurred exposure. ... Direct current (DC or continuous current) is the continuous flow of electricity through a conductor such as a wire from high to low potential. ... In mathematics, the absolute value (or modulus[1]) of a real number is its numerical value without regard to its sign. ...


A cosine wave is said to be "sinusoidal", because: In mathematics, the trigonometric functions are functions of an angle, important when studying triangles and modeling periodic phenomena. ...

cos(x) = sinleft(x +frac{pi}{2}right),

which is also a sine wave with a phase-shift of п/2. Because of this "head start", it is often said that the cosine function leads the sine function or the sine lags the cosine.


Any non-sinusoidal waveforms, such as square waves or even the irregular sound waves made by human speech, can be represented as a collection of sinusoidal waves of different periods and frequencies blended together. The technique of transforming a complex waveform into its sinusoidal components is called Fourier analysis. Non-sinusoidal waveforms are waveforms that are not sine waves. ... A square wave is a kind of basic waveform. ... Speech communication is the aural form of transferring ideas, thoughts, instructions and/or directives utilizing the speakers vocal chords and mouth to stimulate the air, thus causing waves of sound to strike the audible receptors of the hearer, resulting in a transformation back into mental images and/or symbols... Periodicity is the quality of occurring at regular intervals (e. ... FreQuency is a music video game developed by Harmonix and published by SCEI. It was released in November 2001. ... Harmonic analysis is the branch of mathematics which studies the representation of functions or signals as the superposition of basic waves. ...


The human ear can recognize single sine waves because sounds with such a waveform sound "clean" or "clear" to humans; some sounds that approximate a pure sine wave are whistling, a crystal glass set to vibrate by running a wet finger around its rim, and the sound made by a tuning fork. The ear is the sense organ that detects sounds. ... Whistling is the production of sound by means of a constant breath of air from the mouth. ... The materials definition of a glass is a uniform amorphous solid material, usually produced when a suitably viscous molten material cools very rapidly, thereby not giving enough time for a regular crystal lattice to form. ... A tuning fork is a simple metal two-pronged fork with the tines formed from a U-shaped bar of elastic material (usually steel). ...


To the human ear, a sound that is made up of more than one sine wave will either sound "noisy" or will have detectable harmonics; this may be described as a different timbre. In acoustics and telecommunication, the harmonic of a wave is a component frequency of the signal that is an integral multiple of the fundamental frequency. ... In music, timbre, or sometimes timber, (from Fr. ...


Fourier series

In 1822, Joseph Fourier, a French mathematician, discovered that sinusoidal waves can be used as simple building blocks to 'make up' and describe nearly any periodic waveform. The process is named Fourier analysis, which is a useful analytical tool in the study of waves, heat flow, many other scientific fields, and signal processing theory. Also see Fourier series and Fourier transform. Jean Baptiste Joseph Fourier (March 21, 1768 - May 16, 1830) was a French mathematician and physicist who is best known for initiating the investigation of Fourier series and their application to problems of heat flow. ... Harmonic analysis is the branch of mathematics which studies the representation of functions or signals as the superposition of basic waves. ... Signal processing is the processing, amplification and interpretation of signals, and deals with the analysis and manipulation of signals. ... The Fourier series is a mathematical tool used for analyzing periodic functions by decomposing such a function into a weighted sum of much simpler sinusoidal component functions sometimes referred to as normal Fourier modes, or simply modes for short. ... In mathematics, the Fourier transform is a certain linear operator that maps functions to other functions. ...


See also

Sine, square, triangle, and sawtooth waveforms
Sine, square, triangle, and sawtooth waveforms

 
 

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