# What is a Sine Wave

You might be wondering what a sine wave is if you have not heard about it before. However, if you know about it and still want to know more to understand it completely, you have come to the right place.

In this article, I will be explaining what a sine wave is, its properties, importance, and many more. Hence, you would have gotten all the information you sought at the end of this article.

So, sit and relax while I feed you the information.

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## What Is A Sine Wave

Sine Wave is a geometric waveform defined by the function y= sin x. This wave moves up, down, or side to side regularly.

It refers to the graphical representation of the general function. Also, it is a continuous wave, and it is named after the function “sine.”

It often appears in pure and applied mathematics, physics, engineering, signal processing, and many more.

Graphically, a sine wave is a smooth wave that has an s-shape. It usually moves or fluctuates between zero and one.

Generally, we use sine waves in technical analysis and trading to discover oscillator patterns and cross-overs. In trading and technical analysis, the sine-wave indicator is based on the cyclical nature of market movements.

After quantifying a cycle, a trader may construct a leading indicator using the pattern. When the market is going in a process, this method works well.

However, when the market is trending, this system fails (and one should adjust for that)

Furthermore, the market fluctuates between cycle and trending periods. Therefore, price bouncing off support or resistance levels and breakouts or overshoots are under cyclical periods.

Meanwhile, new highs or new lows, as well as pullbacks, are under trending periods. Therefore, the values for these criteria continue in the direction of the trend until they become exhausted.

#### Sine Wave In Technical Analysis

In technical analysis, oscillators with sine-shaped features are frequently used. An oscillator resides between 2 extreme values, and they usually use the result to create a trend indicator.

This trend indicator is, in turn, used to identify short-term overbought or oversold conditions. When the oscillator’s value approaches the upper extreme, analysts take it to suggest that the asset is overbought.

Also, when it approaches the lower extreme, analysts interpret it to mean the asset is oversold.

#### Sine Wave As Analytical Tools

The sine wave is a technical chart analysis tool that uses advanced mathematics to determine if a market is trending or in cycle mode. Also, it helps traders to identify the start and end of a tending move and potential trend changes.

This leading indicator is also known as the MESA indicator. It was created by John Ehlers and is based on an algorithm used in digital signal processing.

The sine wave and the lead wave are the two lines that make up the analysis. These lines do not cross while the price is trending, and they usually run parallel and apart.

Under the right circumstances, line crossovers could identify turning points and provide buy or sell signals. Also, the indicator can indicate whether a market is over-bought or over-sold.

As a result, this might have an impact on the current trend. For a trader, the sine waves are valuable, either employed or in combination with others.

Since the index’s components (ratio and interest rates) tend to swing between a range of values, the composite index of the lagging indicator resembles a sine wave.

Inflation, for example, is constantly kept within a goal range. If inflation meets or exceeds that range for once, interest rates will be modified to either boost or lower inflation.

Therefore, when there is an increase or decrease, the interest rate will fluctuate up and down to keep an undesirable rate of inflation under control.

#### Sinusoidal Waveforms

When an electric current flows through a wire or conductor, it creates a circular magnetic field around it. The intensity of which is proportional to the current magnitude.

If you move or rotate a single wire conductor within a stationary magnetic field, an EMF (Electro-Motive Force) will be induced within the conductor. This will be due to the movement of the conductor through the magnetic flux.

Due to this, we can see that there is a relationship between electricity and magnetism, which gives us the effect of “Electromagnetic Induction” that Michael Faraday discovered.

Electromagnetic induction is the basic principle that electrical devices and generators generate a sine wave for our main supply.

For illustration, let’s assume we have points A to D. When a single wire conductor moves through a permanent magnetic field and results in cutting the lines of flux, an EMT is induced in it.

If, on the contrary, the conductor moves parallel to the magnetic field, as in points A and B, no flux lines are cut, and no EMF is induced into the conductor. However, if the conductor moves at right angles to the magnetic field, as in points C and D, the maximum amount of magnetic flux is cut, producing the total amount of induced EMF.

Furthermore, because the conductor cuts the magnetic field at various angles between points A and C, 0 and 90o, the amount of induced EMF will fall anywhere between zero and maximum.

The quantity of emf induced in a conductor is then determined by the angle between the conductor, the magnetic flux, and the magnetic field’s strength.

#### Sinusoidal Waveform Construction

You can obtain the sinusoidal waveform by projecting across from the various places of rotation between 0o and 360o to the ordinate of the waveform.

Also, when the wire loop or coil rotates one complete, or 360o, one entire waveform is created. Therefore, a generated EMF is 0 when it is equal to 0o, 180o, 360o, as the coil cuts the smallest amount of flux lines.

However, when it is 90o or 270o, the generated EMF reaches its maximum quantity of flux, and it is cut. A sinusoidal waveform thus has a positive peak at 90 degrees and a negative peak at 270 degrees.

The waveform shape generated by a single loop generator is a sine wave since it has a sinusoidal pattern. Since it is based on the trigonometric sine function used in mathematics, (x(t) = Amax. sin), this waveform is termed a sine wave.

Furthermore, when working with sine waves in the time domain, particularly current-relate sine waves, one can measure the horizontal axis of the waveform in time, degrees, or radians.

Radian is commonly used in electrical engineering to measure the angle along the horizontal axis. For example ω = 100 rad/s, or 500 rad/s.

#### What Is Radians

Radians (rad) is a quadrant of a circle in which the distance subtended on the circumference of the circle equals the length of the radius (r) of the same process.

Since the circumference of a circle equals 2π x radius, the 360o of a circle must have 2 radians rather than degrees along the horizontal axis.

In another way, the radian is an angular measurement unit. For example, one radian (r) will fit 6.284 (2*) times around the circumference of a circle.

Thus, one radian is equivalent to 360o/2=57.3o. Radians are so common in electrical engineering, so it is essential to remember the above formula.

## The Sine Wave And Phase

In Basic AC Circuits (Second Edition), 2000.

#### Sine Wave Instantaneous Values

The relationship between the sinusoidal waveform and the trigonometric sine function is useful when determining the instantaneous values of a sinusoidal voltage at any electrical degree.

The equation below expresses numerically the relationship between instantaneous voltage values and the sine function.

Equation 4.1;

ei = Epksinθ

Where ei is the current or voltage value at the electrical degree point theta(θ). Sine of theta(θ) is the value of the trigonometric sine function of electrical degree of point theta.

Epki is the peak value(highest amplitude) of tAmplitudeidal waveform being studied.

For illustration, assuming you want to know the instant amplitude of a Amplitudeeak sinusoidal voltage, 30 degrees into the cycle. You can calculate this using equation 4.1

The sinusoidal waveform is a symmetrical waveform. If the positive peak has a value of 10 volts, then the negative peak will also have a value of 10 volts.

When measuring the peak value of a waveform, you can use either positive or negative peaks.

From equation 4.1;

40 Vsin30°

Resolving it further is = 40 V(0,5)

Which is = 20 V

The instant voltage at 30 degrees is 20 volts.

This calculation is simple since theta(θ) is between 0 and 90 degrees. Therefore, you can easily determine sine theta from almost any trigonometric table.

## AC And The Sine Wave

John Clayton Rawlins M.S., in Basic AC Circuits (Second Edition), 2000

#### Peak Amplitude Specifications

The highest positive or negative departure of a waveform from its zero reference level is the peak amplitude of a sinusoidal waveform.

Note that the highest voltage or current occurs when the wire loop cuts the magnetic flux at a 90-degree angle. Since the sinusoidal waveform is symmetrical, the positive and negative peak values are the same.

Hence, if the positive peak value has a value of 10 volts, the negative peak value will have the same value. So, you can use positive or negative peaks to determine the peak value of a waveform.

#### Resistive Circuits

In calculating instantaneous Voltages and Currents, remember that you can calculate the instant value of the voltage for a sinusoidal waveform using this equation.

ei = Epksintheta — equ (5-2)

The instant voltage is equal to the peak voltage x sine theta. For example, the peak amplitude of a waveform is 10 volts.

Since the Sine of 0 degrees is 0, at 0 degrees the voltage is zero.

At 45 degrees the voltage has increased to 7.07 volts, below is the calculation.

ei = Epksintheta

imputing the figures = (10)(0.707)

Which is = 7.07V

The voltage has risen to 10 volts at 90 degrees. As the angle theta grows, the waveform voltage decreases.

At 135 degrees, the voltage is 7.07 volts again, and at 180 degrees, it is zero. Also, the voltage amplitude varies in the same way that it does in the positive alternation, but with opposite polarities-negative polarities.

## Properties Of Sine Waves

A sine wave is a graph of a sine function. The horizontal axis is the x-axis, and the vertical axis is the y-axis in the graph.

A sinusoid is a graph that has the shape of a sine wave, moving up and down in a regular, continuous manner. Let’s take a little side trip into mathematics to get the right language for discussing sine waves and the sine function.

To start with, we will go over the sine function as it relates to sound, and then we will go over the related terminology.

The sine function represents a single frequency sound wave with frequency f, maximum amplitude A, and phase θ

y=A sin(2πfx + θ )

Where x is time and y is the amplitude of thAmplitudeave at time x.

Sinusoidal waves are single-frequency sound waves. However, pure single-frequency sound waves do not exist in nature.

You can produce them artificially using a computer. Also, naturally occurring sound waves usually consist of frequency components.

Let’s give an illustration, a wave’s amplitude is the amplitude at some point in time, which is x. That is, if we are talking about a pure sine wave, the amplitude A is equal to the wave’s highest y value.

Note that the crest of the wave is what we call this highest value, and the trough is the lowest point on the wave.

Similarly, when air pressure changes as a result of the vibration that produces sound, the change is measured in Newtons/meter2 or, more commonly, in decibels(dB).

The amplitude of a Amplitudee determines how loud it sounds to the human ear.

## The Importance Of Sine Waves

Despite its theoretical relevance, sine waves people rarely use sine waves in the production of music, not conventional music, though. Few instruments produce a sine-wave sound when played normally.

However, sine waves can be a key component of synthesizing sounds in electronic music. Let me explain why they are so important; I will give three reasons.

We use sine waves to define several basic concepts and qualities in the field of sound. Also, they provide us with a basic language for discussing sounds’ physical qualities.

Secondly, they enable us to explore the connections between purely physical qualities of sounds and our subjective experience of hearing them.

They are necessary for the analysis and synthesis of musical sounds (and also non-musically).

## Sine Wave Features

It is clear from the definition that the only waveform that is in the frequency domain is the sine wave. A sine wave in the time domain is a mathematical curve that has a clear definition.

It has 3 terms that fully explain absolutely everything you could ever ask about it. The following 3 terms fully describe a sine wave.

• Frequency
• Amplitude
• Phase

‘f’ is usually used to identify the frequency in Hertz. It is the number of complete cycles per second produced by the sine wave.

We measure angular frequency in radians per second.

A radian is a fraction of a cycle, similar to degrees. In one complete cycle, there are 2 x p radians.

The angular frequency is typically expressed as radians per second, denoted by the Greek letter w.

Furthermore, the frequency of a sine wave and the angular frequency are related by

w= 2π x r

where

w is equal to angular frequency, in radians/sec

π = constant 3.14159

f= sine-wave frequency in Hz

For illustration, if the frequency of a sine wave is 100 MHz, the angular frequency is 2 x 3.14159 x 100 MHz = 6.3 x 10-degree radians\sec.

As for Amplitude, it iAmplitudegest value of the peak height above the center value. The top of the wave goes below as much as it goes above.

Now the Phase – The phase identifies where the wave is in its cycle at the start of the time axis. The unit of phase could be cycle, radians, or degrees.

## Conclusion

A sine wave is a technical tool that advanced mathematicians use to know whether a market is trending or in cycle mode. It is also very important in physics, engineering, and other fields.

We have successfully discussed all you need to know about the Sine wave which includes- What a sine wave is, its properties, its importance, its features, etc.

I hope you found this PowerVersity pick helpful?

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Daniel Gloria Ojone is a Technical Writer at powerversity.com. She has a B.sc in Economics. Gloria loves writing, reading, and dancing. In PowerVersity.com, she writes product best picks, buying guides, and product comparisons.

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