Standing wave in the context of Spherical wave

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.

In physics, mathematics, engineering, and related fields, a wave is a propagating dynamic disturbance (change from equilibrium) of one or more quantities. Periodic waves oscillate repeatedly about an equilibrium (resting) value at some frequency. When the entire waveform moves in one direction, it is said to be a travelling wave; by contrast, a pair of superimposed periodic waves traveling in opposite directions makes a standing wave. In a standing wave, the amplitude of vibration has nulls at some positions where the wave amplitude appears smaller or even zero.

There are two types of waves that are most commonly studied in classical physics: mechanical waves and electromagnetic waves. In a mechanical wave, stress and strain fields oscillate about a mechanical equilibrium. A mechanical wave is a local deformation (strain) in some physical medium that propagates from particle to particle by creating local stresses that cause strain in neighboring particles too. For example, sound waves are variations of the local pressure and particle motion that propagate through the medium. Other examples of mechanical waves are seismic waves, gravity waves, surface waves and string vibrations. In an electromagnetic wave (such as light), coupling between the electric and magnetic fields sustains propagation of waves involving these fields according to Maxwell's equations. Electromagnetic waves can travel through a vacuum and through some dielectric media (at wavelengths where they are considered transparent). Electromagnetic waves, as determined by their frequencies (or wavelengths), have more specific designations including radio waves, infrared radiation, terahertz waves, visible light, ultraviolet radiation, X-rays and gamma rays.

Surfing is a surface water sport in which an individual, a surfer (or two in tandem surfing), uses a board to ride on the forward section, or face, of a moving wave of water, which usually carries the surfer towards the shore. Waves suitable for surfing are primarily found on ocean shores, but can also be found as standing waves in the open ocean, in lakes, in rivers in the form of a tidal bore, or wave pools.

Surfing includes all forms of wave-riding using a board, regardless of the stance. There are several types of boards. The Moche of Peru would often surf on reed craft, while the native peoples of the Pacific surfed waves on alaia, paipo, and other such watercraft. Ancient cultures often surfed on their belly and knees, while modern-day surfing is most often stand-up surfing, in which a surfer rides a wave while standing on a surfboard.

A seiche (/seɪʃ/ SAYSH) is a standing wave in an enclosed or partially enclosed body of water. Seiches and seiche-related phenomena have been observed on lakes, reservoirs, swimming pools, bays, harbors, caves, and seas. The key requirement for formation of a seiche is that the body of water be at least partially bounded, allowing the formation of the standing wave.

The term was promoted in 1890 by the Swiss hydrologist François-Alphonse Forel, who was the first to make scientific observations of the effect in Lake Geneva. The word had apparently long been used in the region to describe oscillations in alpine lakes. According to Wilson (1972), this Swiss French dialect word comes from the Latin word siccus meaning "dry", i.e., as the water recedes, the beach dries. The French word sec or sèche (dry) descends from the Latin.

A vibration in a string is a wave. Initial disturbance (such as plucking or striking) causes a vibrating string to produce a sound with constant frequency, i.e., constant pitch. The nature of this frequency selection process occurs for a stretched string with a finite length, which means that only particular frequencies can survive on this string. If the length, tension, and linear density (e.g., the thickness or material choices) of the string are correctly specified, the sound produced is a musical tone. Vibrating strings are the basis of string instruments such as guitars, cellos, and pianos. For a homogeneous string, the motion is given by the wave equation.

The trumpet is a brass instrument commonly used in classical and jazz ensembles. The trumpet group ranges from the piccolo trumpet—with the highest register in the brass family—to the bass trumpet, pitched one octave below the standard B♭ or C trumpet.

Trumpet-like instruments have historically been used as signaling devices in battle or hunting, with examples dating back to the 2nd Millennium BC. They began to be used as musical instruments only in the late 14th or early 15th century. Trumpets are used in art music styles, appearing in orchestras, concert bands, chamber music groups, and jazz ensembles. They are also common in popular music and are generally included in school bands. Sound is produced by vibrating the lips in a mouthpiece, which starts a standing wave in the air column of the instrument. Since the late 15th century, trumpets have primarily been constructed of brass tubing, usually bent twice into a rounded rectangular shape.

The wave equation is a second-order linear partial differential equation for the description of waves or standing wave fields such as mechanical waves (e.g. water waves, sound waves and seismic waves) or electromagnetic waves (including light waves). It arises in fields like acoustics, electromagnetism, and fluid dynamics.

This article focuses on waves in classical physics. Quantum physics uses an operator-based wave equation often as a relativistic wave equation.

The trombone is a musical instrument in the brass family. As with all brass instruments, sound is produced when the player's lips vibrate inside a mouthpiece, causing the air column inside the instrument to vibrate. Nearly all trombones use a telescoping slide mechanism to alter the pitch instead of the valves used by other brass instruments. The valve trombone is an exception, using three valves similar to those on a trumpet, and the superbone has valves and a slide.

The word trombone derives from Italian tromba (trumpet) and -one (a suffix meaning 'large'), so the name means 'large trumpet'. The trombone has a predominantly cylindrical bore like the trumpet, in contrast to the more conical brass instruments like the cornet, the flugelhorn, the baritone, and the euphonium. The two most frequently encountered variants are the tenor trombone and bass trombone; when the word trombone is mentioned alone; it is mostly taken to mean the tenor model. These are treated as non-transposing instruments, reading at concert pitch in bass clef, with higher notes sometimes being notated in tenor clef. They are pitched in B♭, an octave below the B♭ trumpet and an octave above the B♭ contrabass tuba. The once common E♭ alto trombone became less common as improvements in technique extended the upper range of the tenor, but it is regaining popularity for its lighter sonority. In British brass-band music the tenor trombone is treated as a B♭ transposing instrument, written in treble clef, and the alto trombone is written at concert pitch, usually in alto clef.

In radio and telecommunications a dipole antenna or doubletis one of the two simplest and most widely used types of antenna; the other is the monopole. The dipole is any one of a class of antennas producing a radiation pattern approximating that of an elementary electric dipole with a radiating structure supporting a line current so energized that the current has only one node at each far end. A dipole antenna commonly consists of two identical conductive elementssuch as metal wires or rods. The driving current from the transmitter is applied, or for receiving antennas the output signal to the receiver is taken, between the two halves of the antenna. Each side of the feedline to the transmitter or receiver is connected to one of the conductors. This contrasts with a monopole antenna, which consists of a single rod or conductor with one side of the feedline connected to it, and the other side connected to some type of ground. A common example of a dipole is the rabbit ears television antenna found on broadcast television sets. All dipoles are electrically equivalent to two monopoles mounted end-to-end and fed with opposite phases, with the ground plane between them made virtual by the opposing monopole.

The dipole is the simplest type of antenna from a theoretical point of view. Most commonly it consists of two conductors of equal length oriented end-to-end with the feedline connected between them.Dipoles are frequently used as resonant antennas. If the feedpoint of such an antenna is shorted, then it will be able to resonate at a particular frequency, just like a guitar string that is plucked. Using the antenna at around that frequency is advantageous in terms of feedpoint impedance (and thus standing wave ratio), so its length is determined by the intended wavelength (or frequency) of operation. The most commonly used is the center-fed half-wave dipole which is just under a half-wavelength long. The radiation pattern of the half-wave dipole is maximum perpendicular to the conductor, falling to zero in the axial direction, thus implementing an omnidirectional antenna if installed vertically, or (more commonly) a weakly directional antenna if horizontal.

A wave, in physics, mathematics, engineering and related fields, is a propagating dynamic disturbance (change from equilibrium) of one or more quantities. Periodic waves oscillate repeatedly about an equilibrium (resting) value at some frequency. When the entire waveform moves in one direction, it is said to be a travelling wave; by contrast, a pair of superimposed periodic waves traveling in opposite directions makes a standing wave. In a standing wave, the amplitude of vibration has nulls at some positions where the wave amplitude appears smaller or even zero.

There are two types of waves that are most commonly studied in classical physics: mechanical waves and electromagnetic waves. In a mechanical wave, stress and strain fields oscillate about a mechanical equilibrium. A mechanical wave is a local deformation (strain) in some physical medium that propagates from particle to particle by creating local stresses that cause strain in neighboring particles too. For example, sound waves are variations of the local pressure and particle motion that propagate through the medium. Other examples of mechanical waves are seismic waves, gravity waves, surface waves and string vibrations. In an electromagnetic wave (such as light), coupling between the electric and magnetic fields sustains propagation of waves involving these fields according to Maxwell's equations. Electromagnetic waves can travel through a vacuum and through some dielectric media (at wavelengths where they are considered transparent). Electromagnetic waves, as determined by their frequencies (or wavelengths), have more specific designations including radio waves, infrared radiation, terahertz waves, visible light, ultraviolet radiation, X-rays and gamma rays.

A two-dimensional elastic membrane under tension can support transverse vibrations. The properties of an idealized drumhead can be modeled by the vibrations of a circular membrane of uniform thickness, attached to a rigid frame. Based on the applied boundary condition, at certain vibration frequencies, its natural frequencies, the surface moves in a characteristic pattern of standing waves. This is called a normal mode. A membrane has an infinite number of these normal modes, starting with a lowest frequency one called the fundamental frequency.

There exist infinitely many ways in which a membrane can vibrate, each depending on the shape of the membrane at some initial time, and the transverse velocity of each point on the membrane at that time. The vibrations of the membrane are given by the solutions of the two-dimensional wave equation with Dirichlet boundary conditions which represent the constraint of the frame. It can be shown that any arbitrarily complex vibration of the membrane can be decomposed into a possibly infinite series of the membrane's normal modes. This is analogous to the decomposition of a time signal into a Fourier series.

A node is a point along a standing wave where the wave has minimum amplitude. For instance, in a vibrating guitar string, the ends of the string are nodes. By changing the position of the end node through frets, the guitarist changes the effective length of the vibrating string and thereby the note played. The opposite of a node is an antinode, a point where the amplitude of the standing wave is at maximum. These occur midway between the nodes.

The harmonic series (also overtone series) is the sequence of harmonics, musical tones, or pure tones whose frequency is an integer multiple of a fundamental frequency.

Pitched musical instruments are often based on an acoustic resonator such as a string or a column of air, which oscillates at numerous modes simultaneously. As waves travel in both directions along the string or air column, they reinforce and cancel one another to form standing waves. Interaction with the surrounding air produces audible sound waves, which travel away from the instrument. These frequencies are generally integer multiples, or harmonics, of the fundamental and such multiples form the harmonic series.

Shock diamonds (also known as Mach diamonds or thrust diamonds, and less commonly Mach disks) are a formation of standing wave patterns that appear in the supersonic exhaust plume of an aerospace propulsion system, such as a supersonic jet engine, rocket, ramjet, or scramjet, when it is operated in an atmosphere. The "diamonds" are actually a complex flow field made visible by abrupt changes in local density and pressure as the exhaust passes through a series of standing shock waves and expansion fans. The physicist Ernst Mach was the first to describe a strong shock normal to the direction of fluid flow, the presence of which causes the diamond pattern.