Sine wave in the context of First Point of Aries

Alternating current (AC) is an electric current that periodically reverses direction and changes its magnitude continuously with time, in contrast to direct current (DC), which flows only in one direction. Alternating current is the form in which electric power is delivered to businesses and residences, and it is the form of electrical energy that consumers typically use when they plug kitchen appliances, televisions, fans and electric lamps into a wall socket. The abbreviations AC and DC are often used to mean simply alternating and direct, respectively, as when they modify current or voltage.

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 (the full period is called a cycle). "Alternating current" most commonly refers to power distribution, but a wide range of other applications are technically alternating current although it is less common to describe them by that term. In many applications, like guitar amplifiers, different waveforms are used, such as triangular waves or square waves. Audio and radio signals carried on electrical wires are also examples of alternating current. These types of alternating current carry information such as sound (audio) or images (video) sometimes carried by modulation of an AC carrier signal. These currents typically alternate at higher frequencies than those used in power transmission.

In physics and mathematics, wavelength or spatial period of a wave or periodic function is the distance over which the wave's shape repeats. In other words, it is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, troughs, or zero crossings. Wavelength is a characteristic of both traveling waves and standing waves, as well as other spatial wave patterns. The inverse of the wavelength is called the spatial frequency. Wavelength is commonly designated by the Greek letter lambda (λ). For a modulated wave, wavelength may refer to the carrier wavelength of the signal. The term wavelength may also apply to the repeating envelope of modulated waves or waves formed by interference of several sinusoids.

Assuming a sinusoidal wave moving at a fixed wave speed, wavelength is inversely proportional to the frequency of the wave: waves with higher frequencies have shorter wavelengths, and lower frequencies have longer wavelengths.

Traditionally in Western music, a musical tone is a steady periodic sound. A musical tone is characterized by its duration, pitch, intensity (or loudness), and timbre (or quality). The notes used in music can be more complex than musical tones, as they may include aperiodic aspects, such as attack transients, vibrato, and envelope modulation.

A simple tone, or pure tone, has a sinusoidal waveform. A complex tone is a combination of two or more pure tones that have a periodic pattern of repetition, unless specified otherwise.

A crest point on a wave is the highest point of the wave. A crest is a point on a surface wave where the displacement of the medium is at a maximum. A trough is the opposite of a crest, so the minimum or lowest point of the wave.

When the crests and troughs of two sine waves of equal amplitude and frequency intersect or collide, while being in phase with each other, the result is called constructive interference and the magnitudes double (above and below the line). When in antiphase – 180° out of phase – the result is destructive interference: the resulting wave is the undisturbed line having zero amplitude.

In electronics, acoustics, and related fields, the waveform of a signal is the shape of its graph as a function of time, independent of its time and magnitude scales and of any displacement in time. Periodic waveforms repeat regularly at a constant period. The term can also be used for non-periodic or aperiodic signals, like chirps and pulses.

In electronics, the term is usually applied to time-varying voltages, currents, or electromagnetic fields. In acoustics, it is usually applied to steady periodic sounds — variations of pressure in air or other media. In these cases, the waveform is an attribute that is independent of the frequency, amplitude, or phase shift of the signal.

In mathematics, physics, and engineering, spatial frequency is a characteristic of any structure that is periodic across position in space. The spatial frequency is a measure of how often sinusoidal components (as determined by the Fourier transform) of the structure repeat per unit of distance.

The SI unit of spatial frequency is the reciprocal metre (m), although cycles per meter (c/m) is also common. In image-processing applications, spatial frequency is often expressed in units of cycles per millimeter (c/mm) or also line pairs per millimeter (LP/mm).

Clipping is a form of waveform distortion that occurs when an amplifier is overdriven and attempts to deliver an output voltage or current beyond its maximum capability. Driving an amplifier into clipping may cause it to output power in excess of its power rating.

In the frequency domain, clipping produces strong harmonics in the high-frequency range (as the clipped waveform comes closer to a square wave). The extra high-frequency weighting of the signal could make tweeter damage more likely than if the signal was not clipped.

An overtone is any resonant frequency above the fundamental frequency of a sound (or of any oscillation). An overtone may or may not be a harmonic. In other words, overtones are all pitches higher than the lowest pitch within an individual sound; the fundamental is the lowest pitch. While the fundamental is usually heard most prominently, overtones are actually present in any pitch except a true sine wave. The relative volume or amplitude of various overtone partials is one of the key identifying features of timbre, or the individual characteristic of a sound.

Using the model of Fourier analysis, the fundamental and the overtones together are called partials. Harmonics, or more precisely, harmonic partials, are partials whose frequencies are numerical integer multiples of the fundamental (including the fundamental, which is 1 times itself). These overlapping terms are variously used when discussing the acoustic behavior of musical instruments. (See etymology below.) The model of Fourier analysis provides for the inclusion of inharmonic partials, which are partials whose frequencies are not whole-number ratios of the fundamental (such as 1.1 or 2.14179).

The fundamental frequency, often referred to simply as the fundamental (abbreviated as f₀ or f₁ ), is defined as the lowest frequency of a periodic waveform. In music, the fundamental is the musical pitch of a note that is perceived as the lowest partial present. In terms of a superposition of sinusoids, the fundamental frequency is the lowest frequency sinusoidal in the sum of harmonically related frequencies, or the frequency of the difference between adjacent frequencies. In some contexts, the fundamental is usually abbreviated as f₀, indicating the lowest frequency counting from zero. In other contexts, it is more common to abbreviate it as f₁, the first harmonic. (The second harmonic is then f₂ = 2⋅f₁, etc.)

According to Benward and Saker's Music: In Theory and Practice:

Electric power quality is the degree to which the voltage, frequency, and waveform of a power supply system conform to established specifications. Good power quality can be defined as a steady supply voltage that stays within the prescribed range, steady AC frequency close to the rated value, and smooth voltage curve waveform (which resembles a sine wave). In general, it is useful to consider power quality as the compatibility between what comes out of an electric outlet and the load that is plugged into it. The term is used to describe electric power that drives an electrical load and the load's ability to function properly. Without the proper power, an electrical device (or load) may malfunction, fail prematurely or not operate at all. There are many ways in which electric power can be of poor quality, and many more causes of such poor quality power.

The electric power industry comprises electricity generation (AC power), electric power transmission and ultimately electric power distribution to an electricity meter located at the premises of the end user of the electric power. The electricity then moves through the wiring system of the end user until it reaches the load. The complexity of the system to move electric energy from the point of production to the point of consumption combined with variations in weather, generation, demand and other factors provide many opportunities for the quality of supply to be compromised.

An electronic oscillator is an electronic circuit that produces a periodic, oscillating or alternating current (AC) signal, usually a sine wave, square wave or a triangle wave, powered by a direct current (DC) source. Oscillators are found in many electronic devices, such as radio receivers, television sets, radio and television broadcast transmitters, computers, computer peripherals, cellphones, radar, and many other devices.

Oscillators are often characterized by the frequency of their output signal:

A continuous wave or continuous waveform (CW) is an electromagnetic wave of constant amplitude and frequency, typically a sine wave, that for mathematical analysis is considered to be of infinite duration. It may refer to e.g. a laser or particle accelerator having a continuous output, as opposed to a pulsed output.

By extension, the term continuous wave also refers to an early method of radio transmission in which a sinusoidal carrier wave is switched on and off. This is more precisely called interrupted continuous wave (ICW). Information is carried in the varying duration of the on and off periods of the signal, for example by Morse code in early radio. In early wireless telegraphy radio transmission, CW waves were also known as "undamped waves", to distinguish this method from damped wave signals produced by earlier spark gap type transmitters.

In mathematics, physics, electronics, control systems engineering, and statistics, the frequency domain refers to the analysis of mathematical functions or signals with respect to frequency (and possibly phase), rather than time, as in time series. While a time-domain graph shows how a signal changes over time, a frequency-domain graph shows how the signal is distributed within different frequency bands over a range of frequencies. A complex valued frequency-domain representation consists of both the magnitude and the phase of a set of sinusoids (or other basis waveforms) at the frequency components of the signal. Although it is common to refer to the magnitude portion (the real valued frequency-domain) as the frequency response of a signal, the phase portion is required to uniquely define the signal.

A given function or signal can be converted between the time and frequency domains with a pair of mathematical operators called transforms. An example is the Fourier transform, which converts a time function into a complex valued sum or integral of sine waves of different frequencies, with amplitudes and phases, each of which represents a frequency component. The "spectrum" of frequency components is the frequency-domain representation of the signal. The inverse Fourier transform converts the frequency-domain function back to the time-domain function. A spectrum analyzer is a tool commonly used to visualize electronic signals in the frequency domain.

The first point of Aries, also known as the cusp of Aries or the vernal point, is the location of the March equinox (the vernal equinox in the northern hemisphere, and the autumnal equinox in the southern), used as a reference point in celestial coordinate systems. In diagrams using such coordinate systems, it is often indicated with the symbol ♈︎. Named for the constellation of Aries, it is one of the two points on the celestial sphere at which the celestial equator crosses the ecliptic, the other being the first point of Libra, located exactly 180° from it. Due to precession of the equinoxes since the positions were originally named in antiquity, the position of the Sun when at the March equinox is now in Pisces; when it is at the September equinox, it is in Virgo (as of J2000).

Along its yearly path through the zodiac, the Sun meets the celestial equator as it travels from south to north at the first point of Aries, and from north to south at the first point of Libra. The first point of Aries is considered to be the celestial "prime meridian" from which right ascension is calculated.

Franz Emil Melde (March 11, 1832, in Großenlüder near Fulda – March 17, 1901, in Marburg) was a German physicist and professor. A graduate of the University of Marburg under Christian Ludwig Gerling, he later taught there, focusing primarily on acoustics, also making contributions to fields including fluid mechanics and meteorology. He began in 1860 as Gerling's assistant at the University's Mathematical and Physical Institute, succeeding him in 1864.

Standing waves were first discovered by Melde, who coined the term "standing wave" (stehende Welle) around 1860. What is known as "Melde's experiment", "a lecture-room standby", demonstrates standing waves and their patterns on a string, is used to measure the speed of transverse wave, and to determine the effect of tension, length, and mass on the transverse waves of a string. In 1859 Melde generated parametric oscillations in a string by employing a tuning fork to periodically vary the tension at twice the resonance frequency of the monochord string.

In physics and engineering, the envelope of an oscillating signal is a smooth curve outlining its extremes. The envelope thus generalizes the concept of a constant amplitude into an instantaneous amplitude. The figure illustrates a modulated sine wave varying between an upper envelope and a lower envelope. The envelope function may be a function of time, space, angle, or indeed of any variable.