What Is a Sine Wave?
A sine wave is a geometric waveform that oscillates (moves up, down or side-to-side) periodically, and is defined by the function y = sin x. In other words, it is an s-shaped, smooth wave that oscillates above and below zero.
Sine waves are used in technical analysis and trading to help identify patterns and cross-overs related to oscillators.
Key Takeaways
Understanding Sine Waves
The sine wave indicator is based on the assumption that markets move in cyclical patterns. After quantifying a cycle, a trader may try to use the pattern to develop a leading indicator. This works extremely well when the market is indeed moving in a cycle. When the market is trending, however, this system fails (and one should adjust for that).
Markets alternate between periods of cycling and trending. Cyclical periods are characterized by price bouncing off support or resistance levels and failed breakouts or overshoots. Trending periods are characterized by new highs or new lows and pull backs that then continue in the direction of the trend, until exhausted.
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In technical analysis, oscillators are often used that may have sine-shaped characteristics. An oscillator exists between two extreme values and then builds a trend indicator with the results. The analysts then use the trend indicator to discover short-term overbought or oversold conditions. When the value of the oscillator approaches the upper extreme value, analysts interpret that information to mean that the asset is overbought, and as it approaches the lower extreme, analysts consider the asset to be oversold.
Sine Waves as Analytical Tools
The sine wave as a technical chart analysis tool is based on advanced mathematics and is designed to indicate whether a market is trending or in a cycle mode. It helps traders identify the start and finish of a trending move as well as possible shifts in the trend.
This leading indicator is also called the MESA indicator and was developed by John Ehlers based on an algorithm that was originally applied to digital signal processing. It consists of two lines, called the Sine Wave and the Lead Wave. When the price is trending, the lines do not cross and usually run parallel and distant from each other.
Line crossovers could indicate turning points and generate buy or sell signals under the right conditions. The indicator can also signal an overbought or oversold market (i.e., unjustifiably high or unjustifiably low), which can have implications on the prevailing trend. Whether used alone or in combination with other techniques or non-correlated indicators (such as moving average-based indicators), the sine waves are very useful for a trader.
The Composite Index of Lagging Indicators resembles a sine wave since the measures that make up the index (i.e. ratios and interest rates) tend to oscillate between a range of values.
For example, inflation is always kept between specified rates and if/once inflation meets or exceeds a specified limit, interest rates will be adjusted to either increase or decrease inflation so it is brought within a target range. Thus, as the rate of inflation increases, decreases or stays the same, interest rates will oscillate up and down to control an undesired rate of inflation.
The graphs of the sine (solid red) and cosine (dotted blue) functions are sinusoids of different phases
A sine wave or sinusoid is a mathematical curve that describes a smooth periodic oscillation. A sine wave is a continuous wave. 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:
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 wave shape 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:
which is
The wavenumber is related to the angular frequency by:. https://steelnew.weebly.com/blog/personal-time-tracking-app-mac.
Modified Sine Wave
where λ (lambda) is the wavelength, f is the frequency, and v is the linear speed.
This equation gives a sine wave for a single dimension; thus the generalized equation given above gives the displacement 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 wind waves, sound waves, and light waves.
A cosine wave is said to be sinusoidal, because cosâ¡(x)=sinâ¡(x+Ï/2),{displaystyle cos(x)=sin(x+pi /2),} Electrical circuit diagram software mac. which is also a sine wave with a phase-shift of Ï/2 radians. 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.
To the human ear, a sound that is made of more than one sine wave will have perceptible harmonics; addition of different sine waves results in a different waveform and thus changes the timbre of the sound. Presence of higher harmonics in addition to the fundamental causes variation in the timbre, which is the reason why the same musical note (the same frequency) played on different instruments sounds different. On the other hand, if the sound contains aperiodic waves along with sine waves (which are periodic), then the sound will be perceived to be noisy, as noise is characterized as being aperiodic or having a non-repetitive pattern.
Fourier series[edit]
Sine, square, triangle, and sawtooth waveforms
In 1822, French mathematician Joseph Fourier 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]Sine Pro App
Since sine waves propagate without changing form in distributed linear systems,[definition needed] they are often used to analyze wave propagation. Sine waves traveling in two directions in space can be represented as
Sine Wave Orchestra Mac App Download
When two waves having the same amplitude and frequency, and traveling in opposite directions, superpose each other, then a standing wave pattern is created. Note that, on a plucked string, the interfering waves are the waves reflected from the fixed end points of the string. Therefore, standing waves occur only at certain frequencies, which are referred to as resonant frequencies and are composed of a fundamental frequency and its higher harmonics. The resonant frequencies of a string are proportional to: the length between the fixed ends; the tension of the string; and inversely proportional to the mass per unit length of the string.
See also[edit]![]()
Further reading[edit]Sine Wave Orchestra Mac Apps
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