正弦波

WordNet

an undulating curve (同)undulation
a persistent and widespread unusual weather condition (especially of unusual temperatures); "a heat wave"
set waves in; "she asked the hairdresser to wave her hair"
a movement like that of a sudden occurrence or increase in a specified phenomenon; "a wave of settlers"; "troops advancing in waves"
one of a series of ridges that moves across the surface of a liquid (especially across a large body of water) (同)moving ridge
(physics) a movement up and down or back and forth (同)undulation
the act of signaling by a movement of the hand (同)waving, wafture
a hairdo that creates undulations in the hair
something that rises rapidly; "a wave of emotion swept over him"; "there was a sudden wave of buying before the market closed"; "a wave of conservatism in the country led by the hard right"
commit a sin; violate a law of God or a moral law (同)transgress, trespass
violent and excited activity; "they began to fight like sin" (同)hell
estrangement from god (同)sinfulness, wickedness
an act that is regarded by theologians as a transgression of Gods will (同)sinning
the 21st letter of the Hebrew alphabet
ratio of the length of the side opposite the given angle to the length of the hypotenuse of a right-angled triangle (同)sin
a member of the womens reserve of the United States Navy; originally organized during World War II but now no longer a separate branch

PrepTutorEJDIC

(前後左右・上下に)『揺れる』,ひらめく,ひらひらする / (波形に)『起伏する』,うねる / (手・旗などを振って)『合図する』,手を振る;(…のために,…に向かって)手を振る《+in(to, at)+名》 / (に向かって)‘…を'振る,揺り動かす,ひらめかす《+名+at+名》 / 《方向を表す副詞[句]を伴って》(手・旗などを振って)〈人〉‘に'『合図する』 / ‘…を'起伏させる,うねらせる:〈頭髪〉‘を'ウエーブさせる / 『波』,波浪 / (…の)『波のような動き』,うねり《+of+名》 / (感情・景気などの一時的な)高まり,強まり;(寒暑の)急激な波《+of+名》 / (手・旗などを)振ること,振ってする合図;(…を)振ること《+of+名》 / (髪の)縮れ,ウエーブ / (光・音・電気などの)波
〈U〉(宗教・道徳上の)『罪』 / 〈C〉(宗教・道徳上の)『罪の行為』,罪悪 / 〈C〉《特におどけて》違反(過失)の行為 / (宗教・道徳上の)おきてを破る,罪を犯す / (…に)違反(過失)をする,背く《+『against』+『名』》
sine
(数学で)正弦,サイン(《略》『sin』)

Wikipedia preview

出典(authority):フリー百科事典『ウィキペディア（Wikipedia）』「2013/09/29 01:40:25」(JST)

wiki en

[Wiki en表示]

"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 curve that describes a smooth repetitive oscillation. It is named after the function sine, of which it is the graph. It occurs often in pure and applied mathematics, as well as physics, engineering, signal processing 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 zero.
f, the ordinary frequency, is the number of oscillations (cycles) that occur each second of time.
ω = 2πf, the angular frequency, is the rate of change of the function argument in units of radians per second
φ, the phase, specifies (in radians) where in its cycle the oscillation is at t = 0.
- When φ 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 an advance.

	Sine wave 5 seconds of a 220 Hz sine wave
Problems playing this file? See media help.

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 and magnitude. It is the only periodic waveform that has this property. This property leads to its importance in Fourier analysis and makes it acoustically unique.

General form[edit]

In general, the function may also have:

a spatial dimension, x (aka position), with wavenumber k
a non-zero center amplitude, D

which is

The wavenumber is related to the angular frequency by:.

where λ is the wavelength, f is the frequency, and c is the speed of propagation.

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.

In two or three spatial dimensions, the same equation describes a travelling plane wave if position x and wavenumber k are interpreted as vectors, and their product as a dot product. For more complex waves such as the height of a water wave in a pond after a stone has been dropped in, more complex equations are needed.

Occurrences[edit]

Illustrating the cosine wave's fundamental relationship to the circle.

This wave pattern occurs often in nature, including ocean waves, sound waves, and light waves.

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

The human ear can recognize single sine waves as sounding clear because sine waves are representations of a single frequency with no harmonics; 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.

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.

Fourier series[edit]

Sine, square, triangle, and sawtooth waveforms

Main article: Fourier analysis

In 1822, Joseph Fourier, a French mathematician, discovered that sinusoidal waves can be used as simple building blocks to describe and approximate any periodic waveform including square waves. Fourier used it as an analytical tool in the study of waves and heat flow. It is frequently used in signal processing and the statistical analysis of time series.

Traveling and standing waves[edit]

Since sine waves propagate without changing form in distributed linear systems, they are often used to analyze wave propagation. Sine waves traveling in two directions can be represented as

and

When two waves having the same amplitude and frequency, and traveling in opposite directions, superpose each other, then a standing wave pattern is created.

References[edit]

Hazewinkel, Michiel, ed. (2001), "Sinusoid", Encyclopedia of Mathematics, Springer, ISBN 978-1-55608-010-4 ^{[dead link]}

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English Journal

Perceptual organization of speech signals by children with and without dyslexia.

Nittrouer S, Lowenstein JH.SourceThe Ohio State University, United States. Electronic address: nittrouer.1@osu.edu.
Research in developmental disabilities.Res Dev Disabil.2013 May 20;34(8):2304-2325. doi: 10.1016/j.ridd.2013.04.018. [Epub ahead of print]
Developmental dyslexia is a condition in which children encounter difficulty learning to read in spite of adequate instruction. Although considerable effort has been expended trying to identify the source of the problem, no single solution has been agreed upon. The current study explored a new hypot
PMID 23702597

Identification of the sensory nerve fiber responsible for lysophosphatidic acid-induced allodynia in mice.

Ohsawa M, Miyabe Y, Katsu H, Yamamoto S, Ono H.SourceLaboratory of CNS Pharmacology, Graduate School of Pharmaceutical Sciences, Nagoya City University, 3-1 Tanabe-dori, Mizuho-ku, Nagoya 467-8603, Japan.
Neuroscience.Neuroscience.2013 May 15. pii: S0306-4522(13)00426-0. doi: 10.1016/j.neuroscience.2013.05.014. [Epub ahead of print]
Lysophosphatidic acid (LPA) has been considered one of the molecular culprits for neuropathic pain. Understanding how LPA changes the function of primary afferent fibers might be an essential step for clarifying the pathogenesis of neuropathic pain. The present study was designed to identify the pri
PMID 23685168

Measuring input synchrony in the Ornstein-Uhlenbeck neuronal model through input parameter estimation.

Koutsou A, Kanev J, Christodoulou C.SourceDepartment of Computer Science, University of Cyprus, P.O. Box 20537, 1678 Nicosia, Cyprus. Electronic address: achilleas.k@cs.ucy.ac.cy.
Brain research.Brain Res.2013 May 14. pii: S0006-8993(13)00657-4. doi: 10.1016/j.brainres.2013.05.012. [Epub ahead of print]
We present a method of estimating the input parameters and through them, the input synchrony, of a stochastic leaky integrate-and-fire neuronal model based on the Ornstein-Uhlenbeck process when it is driven by time-dependent sinusoidal input current and noise. By driving the neuron using sinusoidal
PMID 23684712

Japanese Journal

視覚誘導自己直線運動感覚の空間特性の輝度依存性

呉景龍,于英花,楊家家
人間工学 49(1), 18-24, 2013
人間の視野に，一定条件の運動視覚情報を与えることによって，身体が静止状態であるにもかかわらず，自己運動感覚を引き起こすことがある．このことを視覚誘導自己運動感覚と言う．視覚誘導自己運動感覚（Vection）は自己運動感覚の方向によって，大きく二種類に分けられ，視覚誘導自己直線運動感覚（LV：Linear Vection）と視覚誘導自己回転運動感覚（CV：Circular Vection）がある．V …
NAID 130003375666

実機搭載のための画像に基づくファジィ軌道追従制御器のGAによる設計

加藤達也,渡辺桂吾,前山祥一
日本機械学会論文集Ｃ編 79(802), 1970-1979, 2013
… The proposed method is evaluated through some simulations and real robot experiments for a target trajectory consisting of a straight and a sine wave. …
NAID 130003375078

Design of a compact low pass filter for high power RF generators

Park Jaesu,Choi Jaehoon
IEICE Electronics Express 10(2), 20120956-20120956, 2013
… The low-pass filter (LPF) is a key component for high power RF generators generating 40.68MHz sine wave, since the LPF should reject harmonic noises and handle high input power simultaneously. …
NAID 130003364951

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関連記事	「SINE」「sine」「wave」

「SINE」

　　[★]

日: 短い散在反復配列、短分散型核内反復配列、短い散在性反復配列
英: short interspersed element, short interspersed nuclear element, short interspersed nucleotide element, SINEs
関: レトロトランスポゾン

quoted from http://en.wikipedia.org/wiki/Long_interspersed_nucleotide_elements#SINEs

Short interspersed repetitive elements or Short interspersed nuclear elements[8] are short DNA sequences (<500 bases) that represent reverse-transcribed RNA molecules originally transcribed by RNA polymerase III into tRNA, rRNA, and other small nuclear RNAs. SINEs do not encode a functional reverse transcriptase protein and rely on other mobile elements for transposition. The most common SINEs in primates are called Alu sequences. Alu elements are 280 base pairs long, do not contain any coding sequences, and can be recognized by the restriction enzyme AluI (hence the name). With about 1,500,000 copies, SINEs make up about 13% of the human genome.[11] While historically viewed as "junk DNA", recent research suggests that in some rare cases both LINEs and SINEs were incorporated into novel genes, so as to evolve new functionality. The distribution of these elements has been implicated in some genetic diseases and cancers.