A sine wave is an S-shaped waveform defined by the mathematical function y = sin x. It is depicted graphically as two semi-circular curves that alternate above and below a center line.
The graph of y=sin(x) is like a wave that forever oscillates between -1 and 1, in a shape that repeats itself every 2π units. Specifically, this means that the domain of sin(x) is all real numbers, and the range is [-1,1].
Circles are an example of two sine waves
Circles and squares are a combination of basic components (sines and lines). The circle is made from two connected 1-d waves, each moving the horizontal and vertical direction.
Sine Wave. 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.
Sine and cosine are related to circles but are not made of circles. Recall the definition of sine is based on a right triangle inside a circle. sin = opposite / hypotenuse, and cos = adjacent / hypotenuse (SOH CAH TOA).
A full cycle of a periodic sine wave has a value of 360 degrees; therefore, the phase can be measured from zero to 360 degrees. This measurement derives from the trigonometric function of a pure sine tone (Equation 1).
Light waves are definitely sinusoidal. That was conclusively determined by James Maxwell. They actually include both sine waves and cosine waves, one being associated with the energy and the other associated with the momentum of the waves. Very similar to water waves.
People will hear the frequency of a sine wave as pitch, i.e., a high-frequency (often repeating) wave will sound like a high note, while a lower-frequency (not as often repeating) wave will sound like a lower note. Frequency and amplitude are independent of each other.
In real life, though, we don't actually hear sine waves or simple harmonic motion. Rather, sounds that we hear are usually the result of complex vibration in which there are many simultaneous frequencies, amplitudes, and phase differences.
Whistling produces a loud and pitched sound that approximates a sine wave. These sounds travel well over large distances [1] and are easy to discern from other biological sounds by the rare occurrence of pure-tone sine waves in nature.
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.
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.
They are: True Sine Wave (TRUE SINE WAVE) Alternating Current. Modified Sine Wave (MODIFIED SINE WAVE) Alternating Current.
Sine and cosine functions can be used to model many real-life scenarios – radio waves, tides, musical tones, electrical currents.
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.
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.
The cello is said to have the same range as the human voice. This feature gives it the power to evoke instinctual emotions. Songs can be transcribed from voice to cello, and the voice can find itself even within the sound of steel strings.
In general, the fundamental frequency of the complex speech tone – also known as the pitch or f0 – lies in the range of 100-120 Hz for men, but variations outside this range can occur. The f0 for women is found approximately one octave higher. For children, f0 is around 300 Hz.
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. It is sometimes referred to as flat noise as it has equal energy distribution and when plotted on a graph, white noise appears flat and equal.
The commonly stated range of human hearing is 20 to 20,000 Hz. Under ideal laboratory conditions, humans can hear sound as low as 12 Hz and as high as 28 kHz, though the threshold increases sharply at 15 kHz in adults, corresponding to the last auditory channel of the cochlea.
For a single-frequency sound wave, the rate at which it does this is regular and continuous, taking the shape of a sine wave. Thus, the graph of a sound wave is a simple sine wave only if the sound has only one frequency component in it – that is, just one pitch.
The usual waveform of alternating current in most electric power circuits is a sine wave, whose positive half-period corresponds with positive direction of the current and vice versa.
Basically, it's safe to assume that there are ONLY sine waves in nature, and everything else is composed of sine waves.
Radio Wave Basics
Put simply, a radio wave is an electromagnetic wave. It can propagate through a vacuum, air, liquid, or even solid objects. It can be depicted mathematically as a sinusoidal curve as shown in Figure 1-5. The distance covered by a complete sine wave (a cycle) is known as the wavelength .