As the coil rotates the voltage decreases according to the sine of the angle until the conductor is parallel to the magnetic field. Further rotation then increases the voltage until once again it is at a maximum (but in the opposite direction). For each revolution a complete sine wave is generated.
As a conductor passes through a magnetic field a voltage is generated. If that conductor is made into a loop and spun continually through the field a sine wave is generated.
In trigonometry, the name “sine” comes through Latin from a Sanskrit word meaning “chord”. In the picture of a unit circle below, AB has length sinθ and this is half a chord of the circle. The co-functions are functions of complementary angles: cosθ = sin(π/2 − θ), cotθ = tan(π/2 − θ), and cscθ = sec(π/2 − θ).
As we can see, the sine wave "begins" at the origin, climbs to a maximum value of y=1, passes through y=0, descends to a minimum value of y=-1, and then returns to y=0 before repeating that process.
A sine wave or sinusoidal wave is the most natural representation of how many things in nature change state. A sine wave shows how the amplitude of a variable changes with time.
Plot of Sine
The Sine Function has this beautiful up-down curve (which repeats every 2π radians, or 360°). It starts at 0, heads up to 1 by π/2 radians (90°) and then heads down to −1.
Why do we see sine waves in nature so often? When you graph simple harmonic motion, you get sine and cosine waves. There are lots of examples of simple harmonic motion in nature, so we get lots of sine and cosine waves from nature.
For the angle α, the sine gives the ratio of the length of the opposite side to the length of the hypotenuse. The cosine gives the ratio of the length of the adjacent side to the length of the hypotenuse. (Image by Dnu72 – CC BY-SA 3.0.)
A line graph of the Sun's declination during a year resembles a sine wave with an amplitude of 23.44°, but one lobe of the wave is several days longer than the other, among other differences.
All sounds in nature are fundamentally constructed of sine waves. More complex sounds simply contain more oscillations at different frequencies, stacked one upon another. Higher-frequency, oscillations which are tonally related to the fundamental frequency (the base note or tone) are known as harmonics.
It helps to begin by visualizing an acoustical waveform as a sine wave. At the same time, it must be kept in mind that sounds composed of single sine waves (i.e., pure tones) are extremely rare in nature; most sounds in speech, for example, consist of acoustically complex waveforms.
More modern definitions express the sine and cosine as infinite series, or as the solutions of certain differential equations, allowing their extension to arbitrary positive and negative values and even to complex numbers.
Sine was introduced by Abu'l Wafa in 8th century, as a more convenient function, and gradually spread first in the Muslim world, and then to the West. (But apparently it was used in India centuries before him), as a more convenient function. However this new notation was adopted very slowly, it took centuries.
As described above, the air pressure rises and falls. For a single-frequency sound wave, the rate at which it does this is regular and continuous, taking the shape of a sine wave.
This reflects the contrapuntal whistling of the tones accompanying the sequence of syllables, for no natural talker ever produces anything approximate to sine-wave speech.
This combination of many sines waves that are all integer multiples of the fundamental is what gives a piano its distinctive sound. If just the fundamental sine wave vibrated when you pressed a key, it would sound like a cheap alarm clock.
A sine wave has a single frequency component: a fundamental harmonic with absolutely no overtones. If dissected into harmonic components, white noise, on the other hand, contains every frequency, amplitude, and phase relation of a sine wave throughout the audible spectrum.
DEFINITION: A sine wave sounds like it looks: smooth and clean. It is sound at its most basic. The sound of a sine wave is only made up of one thing, something known as the fundamental. No partials to be seen!
Sound and water waves, for example, can be represented as sinusoids, and simple harmonic motion—such as that of a pendulum or a weight attached to a spring—results in a sinusoidal relationship between position and time.
The sound wave from the flute is very smooth and looks like a sine wave from a mathematics textbook. A flute has a strong fundamental frequency of 262 Hz and practically no other harmonics or overtones. A musician might describe a flute as having a very pure tone.
As the given signal x(t) is a squared sine wave, it is a periodic signal, so it can be a power signal.
The exact shape of a sine wave is very important to the field of electronics because it is the only wave shape that has energy at only one frequency. All other possible wave shapes contain energy at more than one frequency at the same time.
As we learned, sine is one of the main trigonometric functions and is defined as the ratio of the side of the angle opposite the angle divided by the hypotenuse. It's important for finding distances or height and can also be used to find angle measures, which are measured in radians.