133:
280:
1883:
43:
1640:
1568:
257:, the result is another sine wave of the same frequency; this property is unique among periodic waves. Conversely, if some phase is chosen as a zero reference, a sine wave of arbitrary phase can be written as the linear combination of two sine waves with phases of zero and a quarter cycle, the
1878:{\displaystyle {\begin{aligned}\int A\sin(\omega t+\varphi )dt&=-{\frac {A}{\omega }}\cos(\omega t+\varphi )+C\\&=-{\frac {A}{\omega }}\sin(\omega t+\varphi +{\tfrac {\pi }{2}})+C\\&={\frac {A}{\omega }}\sin(\omega t+\varphi -{\tfrac {\pi }{2}})+C\,.\end{aligned}}}
729:
1930:'s stopband, although an integrator doesn't have a cutoff frequency or a flat passband. A n-order low-pass filter approximately performs the n time integral of signals whose frequency band is significantly higher than the filter's cutoff frequency.
921:
1404:
461:
1925:
at the origin of the complex frequency plane. The gain of its frequency response falls off at a rate of -20 dB per decade of frequency (for root-power quantities), the same negative slope as a 1 order
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1563:{\displaystyle {\begin{aligned}{\frac {d}{dt}}&=A\omega \cos(\omega t+\varphi )\\&=A\omega \sin(\omega t+\varphi +{\tfrac {\pi }{2}})\,.\end{aligned}}}
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371:
53:
1159:
frequencies are the string's only possible standing waves, which only occur for wavelengths that are twice the string's length (corresponding to the
298:
1282:. 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.
1399:
any sinusoid with respect to time can be viewed as multiplying its amplitude by its angular frequency and advancing it by a quarter cycle:
2126:
297:
1990:
1635:
any sinusoid with respect to time can be viewed as dividing its amplitude by its angular frequency and delaying it a quarter cycle:
1995:
344:. Adding sine waves of different frequencies results in a different waveform. Presence of higher harmonics in addition to the
68:
1970:
1155:
On a plucked string, the superimposing waves are the waves reflected from the fixed endpoints of the string. The string's
1353:
discovered that sinusoidal waves can be summed as simple building blocks to approximate any periodic waveform, including
1039:
963:
111:
83:
665:
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90:
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of time and of the distance from some fixed plane. It is also called a monochromatic plane wave, with constant
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decomposes general functions into a sum of sine waves of various frequencies, relative phases, and magnitudes.
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while going around the circle results in a sine wave (red). Tracing the x component results in a
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along a single line. This could, for example, be considered the value of a wave along a wire.
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seconds. A negative value represents a delay, and a positive value represents an advance.
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916:{\textstyle k{=}{\frac {\omega }{v}}{=}{\frac {2\pi f}{v}}{=}{\frac {2\pi }{\lambda }}}
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is non-zero, the entire waveform appears to be shifted backwards in time by the amount
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then extended
Fourier series to handle general functions, and birthed the field of
600:
296:
144:
wave (blue). Both waves are sinusoids of the same frequency but different phases.
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1624:
whose frequency band is significantly lower than the filter's cutoff frequency.
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In two or three spatial dimensions, the same equation describes a travelling
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1620:. A n-order high-pass filter approximately applies the n time derivative of
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456:{\displaystyle y(t)=A\sin(\omega t+\varphi )=A\sin(2\pi ft+\varphi )}
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Depending on their direction of travel, they can take the form:
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oscillating around the equilibrium over time is a sine wave.
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60:
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Sinusoids that exist in both position and time also have:
559:, the rate of change of the function argument in units of
717:(one cycle) to the phase results in an equivalent wave.
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Sine waves of arbitrary phase and amplitude are called
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Since sine waves propagate without changing form in
1278:are interpreted as vectors, and their product as a
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30:"Sinusoid" redirects here. Not to be confused with
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1877:
1604:quantities), the same positive slope as a 1 order
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1183:
1103:{\displaystyle y(x,t)=A\sin(kx+\omega t+\varphi )}
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1027:{\displaystyle y(x,t)=A\sin(kx-\omega t+\varphi )}
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935:
915:
845:wavenumber is related to the angular frequency by
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356:played on different instruments sounds different.
1914:is an integer multiple of the sinusoid's period.
304:Five seconds of a 220 Hz sine wave. This is the
494:, the peak deviation of the function from zero.
768:on the dimension on which the wave propagates.
2120:
1387:Phasor § Differentiation and integration
8:
1171:The earlier equation gives the displacement
684:{\displaystyle {\tfrac {\varphi }{\omega }}}
69:introducing citations to additional sources
1612:, although a differentiator doesn't have a
635:) where in its cycle the oscillation is at
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1034:, if the wave is moving to the right, or
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59:Relevant discussion may be found on the
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724:As a function of both position and time
319:
7:
1110:, if the wave is moving to the left.
245:When any two sine waves of the same
352:, which is the reason why the same
1991:In-phase and quadrature components
308:described by a sine function with
27:Wave shaped like the sine function
25:
1144:traveling in opposite directions
1118:, they are often used to analyze
603:) that occur each second of time.
1592:increases at a rate of +20
1365:and the statistical analysis of
1291:This section is an excerpt from
732:The displacement of an undamped
329:A sine wave represents a single
320:Problems playing this file? See
294:
52:relies largely or entirely on a
41:
1996:Least-squares spectral analysis
1381:Differentiation and integration
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312:= 220 oscillations per second.
1:
2038:the sine wave symbol (U+223F)
1971:Harmonic series (mathematics)
1136:When two waves with the same
136:Tracing the y component of a
206:. Sine waves occur often in
1167:Multiple spatial dimensions
368:and have the general form:
2236:
1384:
1334:
1290:
1191:of the wave at a position
1129:
1116:distributed linear systems
29:
2142:
775:(or angular wave number)
1314:whose value varies as a
936:{\displaystyle \lambda }
655:{\displaystyle \varphi }
618:{\displaystyle \varphi }
348:causes variation in the
1976:Harmonic series (music)
1889:constant of integration
1361:are frequently used in
1324:monochromatic radiation
811:{\displaystyle \omega }
546:{\displaystyle \omega }
523:, usually representing
224:monochromatic radiation
203:uniform circular motion
32:Sinusoid (blood vessel)
2091:Mathematical Mysteries
2016:Simple harmonic motion
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694:Adding or subtracting
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193:simple harmonic motion
145:
2057:Smith, Julius Orion.
1912:bounds of integration
1905:
1880:
1580:at the origin of the
1565:
1349:French mathematician
1306:is a special case of
1304:sinusoidal plane wave
1293:Sinusoidal plane wave
1286:Sinusoidal plane wave
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1253:
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1186:
1161:fundamental frequency
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710:{\displaystyle 2\pi }
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337:and is considered an
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1910:will be zero if the
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1195:
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1152:pattern is created.
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820:speed of propagation
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764:that represents the
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646:
609:
570:
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521:independent variable
500:
471:
372:
200:, it corresponds to
65:improve this article
1986:Instantaneous phase
1946:Complex exponential
1316:sinusoidal function
1148:each other, then a
744:a spatial variable
190:over time, this is
2063:ccrma.stanford.edu
1981:Helmholtz equation
1900:
1875:
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1600:of frequency (for
1590:frequency response
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734:spring-mass system
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590:ordinary frequency
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561:radians per second
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1966:Harmonic analysis
1961:Fourier transform
1903:{\displaystyle C}
1855:
1820:
1790:
1755:
1702:
1582:complex frequency
1546:
1425:
1371:Fourier transform
1363:signal processing
1341:Fourier transform
1271:{\displaystyle k}
1251:{\displaystyle x}
1224:{\displaystyle t}
1204:{\displaystyle x}
1184:{\displaystyle y}
911:
891:
868:
835:{\displaystyle v}
797:angular frequency
788:{\displaystyle k}
757:{\displaystyle x}
678:
599:of oscillations (
579:{\displaystyle f}
556:angular frequency
509:{\displaystyle t}
480:{\displaystyle A}
299:
255:linearly combined
232:signal processing
130:
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115:
16:(Redirected from
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2157:Rectangular wave
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2021:Sinusoidal model
1951:Damped sine wave
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1614:cutoff frequency
1606:high-pass filter
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1375:Fourier analysis
1345:Fourier analysis
1331:Fourier analysis
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1120:wave propagation
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240:Fourier analysis
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1956:Euler's formula
1941:Crest (physics)
1936:
1928:low-pass filter
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1397:Differentiating
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1392:Differentiation
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1383:
1347:
1335:Main articles:
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1260:
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1258:and wavenumber
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249:(but arbitrary
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175:(shape) is the
154:sinusoidal wave
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2200:Wave mechanics
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2080:External links
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2026:Wave (physics)
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1359:Fourier series
1351:Joseph Fourier
1337:Fourier series
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1130:Main article:
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1126:Standing waves
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63:. Please help
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2031:Wave equation
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360:Sinusoid form
359:
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354:musical pitch
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272:Audio example
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82: –
81:
77:
76:Find sources:
70:
66:
62:
56:
55:
54:single source
50:This article
48:
44:
39:
38:
33:
19:
2195:Trigonometry
2146:
2095:. Retrieved
2093:. 2021-11-17
2090:
2066:. Retrieved
2062:
2052:
2001:Oscilloscope
1916:
1886:
1637:
1631:
1571:
1401:
1395:
1355:square waves
1348:
1238:if position
1233:
1170:
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956:
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739:
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339:acoustically
328:
309:
262:
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210:, including
201:
191:
161:
157:
153:
149:
147:
121:January 2024
118:
108:
101:
94:
87:
75:
51:
2167:Square wave
2087:"Sine Wave"
2059:"Sinusoids"
1633:Integrating
1628:Integration
1584:plane. The
1367:time series
1280:dot product
773:wave number
346:fundamental
236:mathematics
228:engineering
218:waves, and
80:"Sine wave"
2189:Categories
2097:2022-09-30
2068:2024-01-05
2044:References
1919:integrator
1616:or a flat
1602:root-power
1385:See also:
1308:plane wave
1236:plane wave
949:wavelength
322:media help
306:sound wave
266:components
212:wind waves
91:newspapers
2220:Acoustics
2210:Waveforms
2147:Sine wave
2136:Waveforms
2011:Pure tone
1850:π
1844:−
1841:φ
1832:ω
1826:
1818:ω
1785:π
1776:φ
1767:ω
1761:
1753:ω
1745:−
1723:φ
1714:ω
1708:
1700:ω
1692:−
1673:φ
1664:ω
1658:
1649:∫
1541:π
1532:φ
1523:ω
1517:
1511:ω
1492:φ
1483:ω
1477:
1471:ω
1452:φ
1443:ω
1437:
1320:frequency
1146:superpose
1142:frequency
1138:amplitude
1095:φ
1086:ω
1071:
1019:φ
1010:ω
1007:−
995:
947:) is the
931:λ
909:λ
905:π
882:π
863:ω
806:ω
705:π
676:ω
673:φ
650:φ
613:φ
541:ω
491:amplitude
448:φ
436:π
427:
412:φ
403:ω
397:
366:sinusoids
342:pure tone
335:harmonics
331:frequency
290:Sine wave
247:frequency
184:mechanics
160:(symbol:
150:sine wave
61:talk page
18:Sine tone
1934:See also
1618:passband
1610:stopband
1357:. These
1211:at time
1157:resonant
766:position
333:with no
198:rotation
173:waveform
166:periodic
158:sinusoid
1622:signals
1588:of its
1322:(as in
1300:physics
633:radians
529:seconds
463:where:
208:physics
164:) is a
105:scholar
2006:Phasor
1921:has a
1598:decade
1576:has a
1369:. The
1343:, and
945:lambda
923:where
601:cycles
596:number
593:, the
516:, the
350:timbre
263:cosine
253:) are
234:, and
188:motion
171:whose
142:cosine
138:circle
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78:
2215:Sound
2205:Waves
1312:field
642:When
639:= 0.
628:phase
251:phase
226:. In
220:light
216:sound
196:; as
182:. In
156:, or
112:JSTOR
98:books
1923:pole
1887:The
1596:per
1586:gain
1578:zero
1310:: a
1302:, a
1140:and
525:time
518:real
261:and
259:sine
169:wave
84:news
1917:An
1823:sin
1758:sin
1705:cos
1655:sin
1608:'s
1514:sin
1474:cos
1434:sin
1298:In
1068:sin
992:sin
527:in
424:sin
394:sin
67:by
2191::
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109:·
102:·
95:·
88:·
71:.
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34:.
20:)
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