# standing wave

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Standing waves and hydraulic jumps also form on fast flowing river rapids and tidal currents such as the Saltstraumen maelstrom.

In practice, losses in the transmission line and other components mean that a perfect reflection and a pure standing wave are never achieved. The result is a partial standing wave, which is a superposition of a standing wave and a travelling wave. The degree to which the wave resembles either a pure standing wave or a pure travelling wave is measured by the standing wave ratio (SWR).

The equation of a standing wave is represented as follows:

Two waves with the same frequency, wavelength and amplitude traveling in opposite directions will interfere and produce

and

where

So the resultant wave equation will be:

Using a trigonometric identity to simplify,

where y

At

As most commonly used, the term

The

**standing wave**, also known as a*stationary wave*, is a wave that remains in a constant position. This phenomenon can occur because the medium is moving in the opposite direction to the wave, or it can arise in a stationary medium as a result of interference between two waves traveling in opposite directions. There is no net propagation of energy.## Moving medium

As an example of the first type, under certain meteorological conditions standing waves form in the atmosphere in the lee of mountain ranges. Such waves are often exploited by glider pilots.Standing waves and hydraulic jumps also form on fast flowing river rapids and tidal currents such as the Saltstraumen maelstrom.

## Opposing waves

As an example of the second type, a*standing wave*in a transmission line is a wave in which the distribution of current, voltage, or field strength is formed by the superposition of two waves propagating in opposite directions. The effect is a series of nodes (zero displacement) and anti-nodes (maximum displacement) at fixed points along the transmission line. Such a standing wave may be formed when a wave is transmitted into one end of a transmission line and is reflected from the other end by an impedance mismatch,*i.e.*, discontinuity, such as an open circuit or a short. The failure of the line to transfer power at the standing wave frequency will usually result in attenuation distortion.In practice, losses in the transmission line and other components mean that a perfect reflection and a pure standing wave are never achieved. The result is a partial standing wave, which is a superposition of a standing wave and a travelling wave. The degree to which the wave resembles either a pure standing wave or a pure travelling wave is measured by the standing wave ratio (SWR).

The equation of a standing wave is represented as follows:

Two waves with the same frequency, wavelength and amplitude traveling in opposite directions will interfere and produce

**standing wave or stationary wave**.For example a harmonic wave travelling to the right and hitting the end of the string produces standing wave. The reflective wave has to have the same amplitude and frequency as the incoming wave. Let the harmonic waves be represented by the equations below:and

where

**k=2π/λ**So the resultant wave equation will be:

Using a trigonometric identity to simplify,

where y

_{0}is the amplitude of the wave, ω (called*angular frequency*, measured in**radians per second**) is 2π times the frequency (in Hz), k (called the*wave number*and measured in**radians per metre**) is 2π divided by the wavelength (in meters), and x and t are variables for longitudinal position and time, respectively.At

**nodes****x=0,λ/2,λ,3λ/2....**etc. whereas at**antinodes****x=λ/4,3λ/4,5λ/4....**etc. The distance between two conjugative nodes or antinodes is**λ/2**.## Physical waves

Standing waves are also observed in physical media such as strings and columns of air. Any waves travelling along the medium will reflect back when they reach the end. This effect is most noticeable in musical instruments where, at various multiples of a vibrating string or air column's natural frequency, a standing wave is created, allowing harmonics to be identified. Nodes occur at fixed ends and antinodes at open ends. If fixed at only one end, only odd-numbered harmonics are available.## Optical waves

Standing waves are also observed in optical media such as optical wave guides, optical cavities, etc. In an optical cavity, the light wave from one end is made to reflect from the other. The transmitted and reflected waves superpose, and form a standing-wave pattern.## See also

**List of wave topics**: Wave, Amphidromic point, Voltage standing wave ratio, Trumpet, Longitudinal mode, Modelocking, Seiche**List of electronics topics**: Impedance, Federal Standard 1037C, Normal mode, Cavity resonator, Characteristic impedance, Cymatics**People**: Nikola Tesla

## External links

- Vibrations and Waves - a chapter from an online textbook
- Standing Waves experiment Shows how the point moves with frequency change.
- Java applet of standing waves on a vibrating string.

**wave**is a mode of energy transfer from one place to another, often with little or no permanent displacement of the particles of the medium (i.e. little or no associated mass transport); instead there are oscillations around almost fixed positions.

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**Interference**is the addition (superposition) of two or more waves that results in a new wave pattern.

As most commonly used, the term

**interference**usually refers to the interaction of waves which are correlated or coherent with each other, either because they

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**lee waves**, are atmospheric standing waves. The most common form is

**mountain waves**, which are atmospheric internal gravity waves, and were discovered in 1933 by German glider pilots above the Riesengebirge.

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**Gliding**is a recreational activity and competitive sport in which pilots fly un-powered aircraft known as gliders or sailplanes. Properly, the term

*gliding*refers to descending flight of a heavier-than-air craft, whereas

*soaring*

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**hydraulic Jump**is a phenomenon in the science of hydraulics, frequently observed in open channel flow. When liquid at high velocity discharges into a zone of lower velocity, a rather abrupt rise (a step or standing wave) occurs in the liquid surface.

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**RAPID**is an acronym for Rural Address Property IDentification, a scheme instituted in New Zealand to assist emergency services in identifying and locating rural properties.

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**Saltstraumen**is a sound with a strong tidal current located in Nordland some 30 km east of the city of Bodø, Norway. It is the strongest tidal current in the world. Up to 400 million m³ of seawater forces its way through a 3 km long and 150 m wide strait every six hours, with

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A

**maelstrom**(or**malström**) is a very powerful whirlpool; a large, swirling body of water. The word was introduced from the Nordic form by Edgar Allan Poe in his story A Descent into the Maelstrom (1841).**.....**Click the link for more information. A

**transmission line**is the material medium or structure that forms all or part of a path from one place to another for directing the transmission of energy, such as electromagnetic waves or acoustic waves, as well as electric power transmission.**.....**Click the link for more information.**Electric current**is the flow (movement) of electric charge. The SI unit of electric current is the ampere (A), which is equal to a flow of one coulomb of charge per second.

## Definition

The amount of electric current (measured in amperes) through some surface, e.g.**.....**Click the link for more information.

**Voltage**(sometimes also called

*electric potential difference*or

*electrical tension*) is the potential similarity of electrical potential between two points of an electrical or electronic circuit, expressed in volts.

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In physics, the

In theoretical physics, the field strength is another name for the curvature form. For the electromagnetic field, the curvature form is an antisymmetric matrix whose elements are the electric

**field strength**of a field is the magnitude of its vector value.In theoretical physics, the field strength is another name for the curvature form. For the electromagnetic field, the curvature form is an antisymmetric matrix whose elements are the electric

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In physics and mathematics it may refer to the overlapping of waves, or to the overlapping of solutions to linear differential equations:

*superposition*can have several meanings:In physics and mathematics it may refer to the overlapping of waves, or to the overlapping of solutions to linear differential equations:

- The combination of sound or light waves

**.....**Click the link for more information.**Particle displacement**or

**particle amplitude**(represented in mathematics by the lower-case Greek letter ξ) is a measurement of distance (in metres) of the movement of a particle in a medium as it transmits a wave.

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**Particle displacement**or

**particle amplitude**(represented in mathematics by the lower-case Greek letter ξ) is a measurement of distance (in metres) of the movement of a particle in a medium as it transmits a wave.

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**Signal reflection**occurs because when a signal is transmitted along a transmission medium, such as a copper cable or an optical fibre, there is the possibility that some of the signal power will be reflected back to its origin, rather than being carried all the way along the cable

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**Electrical impedance**, or simply

**impedance**, describes a measure of opposition to a sinusoidal alternating current (AC). Electrical impedance extends the concept of resistance to AC circuits, describing not only the relative magnitudes of the voltage and current, but also the

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**Impedance matching**is the practice of attempting to make the output impedance of a source equal to the input impedance of the load to which it is ultimately connected, usually in order to maximize the power transfer and minimize reflections from the load.

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**Discontinuity**can be:

- Discontinuity (mathematics), a feature of a mathematical function

**Discontinuity**may also refer to:

- A break in continuity (fiction), in literature
- Fracture (geology), discontinuity in rocks

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The term

**Open circuit**may refer to:- Open-circuit voltage, the difference of electrical potential between two terminals of a device when there is no external load connected

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**short circuit**(sometimes abbreviated to**short**or**s/c**) allows a charge to flow along a different path from the one intended. The electrical opposite of a*short circuit*is an*open circuit*, which is infinite resistance between two nodes.**.....**Click the link for more information.**Attenuation distortion**

^{[1]}is the distortion of an analog signal that occurs during transmission when the transmission medium does not have a flat frequency response across the bandwidth of the medium or the frequency spectrum of the signal.

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In telecommunications,

**standing wave ratio**(**SWR**) is the ratio of the amplitude of a partial standing wave at an antinode (maximum) to the amplitude at an adjacent node (minimum), in an electrical transmission line.**.....**Click the link for more information.**vibrating string**produces a sound whose frequency in most cases is constant. Therefore, since frequency characterizes the pitch, the sound produced is a constant note. Vibrating strings are the basis of any string instrument like guitar, cello, or piano.

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**fundamental tone**, often referred to simply as the

**fundamental**and abbreviated

**f**, is the lowest frequency in a harmonic series.

_{o}The

**fundamental frequency**(also called a

**natural frequency**

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**harmonic**of a wave is a component frequency of the signal that is an integer multiple of the fundamental frequency. For example, if the frequency is

*f*, the harmonics have frequency 2

*f*, 3

*f*, 4

*f*, etc.

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An

**optical cavity**or**optical resonator**is an arrangement of mirrors that forms a standing wave cavity resonator for light waves. Optical cavities are a major component of lasers, surrounding the gain medium and providing feedback of the laser light.**.....**Click the link for more information. An

**optical cavity**or**optical resonator**is an arrangement of mirrors that forms a standing wave cavity resonator for light waves. Optical cavities are a major component of lasers, surrounding the gain medium and providing feedback of the laser light.**.....**Click the link for more information. This is a

**list of wave topics**, by Wikipedia page.**:**Top - 0–9 A B C D E F G H I J K L M N O P Q R S T U V W X Y Z## 0-9

- 21 cm line
- 4 o'clock wave

## A

- Abbe prism
- absorption spectrum
- Airy disc
- Alfvén wave

**.....**Click the link for more information.**wave**is a mode of energy transfer from one place to another, often with little or no permanent displacement of the particles of the medium (i.e. little or no associated mass transport); instead there are oscillations around almost fixed positions.

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