Vibration and standing waves in a string, The fundamental and the first 6 overtones

A 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. Image File history File links Metadata Size of this preview: 576 × 599 pixelsFull resolution (6064 × 6309 pixel, file size: 1,016 KB, MIME type: image/jpeg) This is image is made by me and everybody is allowed to use it. ... Image File history File links Metadata Size of this preview: 576 × 599 pixelsFull resolution (6064 × 6309 pixel, file size: 1,016 KB, MIME type: image/jpeg) This is image is made by me and everybody is allowed to use it. ... Look up vibration in Wiktionary, the free dictionary. ... A fundamental is something that cannot be built out of more basic things, which other things are built upon. ... An overtone is a sinusoidal component of a waveform, of greater frequency than its fundamental frequency. ... A wave is a disturbance that propagates through space or spacetime, transferring energy and momentum and sometimes angular momentum. ... Interference of two circular waves - Wavelength (decreasing bottom to top) and Wave centers distance (increasing to the right). ...

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. Categories: Aeronautics | Meteorology | Stub ... A modern glider crossing the finish line of a competition at high speed. ...

Standing waves and hydraulic jumps also form on fast flowing river rapids and tidal currents such as the Saltstraumen maelstrom. In the animation, you can see a hydraulic jump appear on the downstream side of the sill. ... ... Saltstraumen, Norway. ... Saltstraumen maelstrom A maelstrom (or malström) is a very powerful whirlpool; a large, swirling body of water. ...

Opposing waves

Standing wave in stationary medium. The red dots represent the wave nodes

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. Animation of a standing wave. ... A standing wave. ... 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. ... In electricity, current refers to electric current, which is the flow of electric charge. ... International safety symbol Caution, risk of electric shock (ISO 3864), colloquially known as high voltage symbol. ... ʐIn physics, the field strength of a field is the magnitude of its vector (spatial) value. ... The term superposition can have several meanings: Quantum superposition Law of superposition in geology and archaeology Superposition principle for vector fields Superposition Calculus is used for equational first-order reasoning This is a disambiguation page — a navigational aid which lists other pages that might otherwise share the same title. ... 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. ... 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. ... Reflection in electricity is the result of impedance mismatch in electrical signals. ... Electrical impedance, or simply impedance, is a measure of opposition to a sinusoidal alternating electric current. ... Impedance mismatch has two meanings. ... In mathematics, a continuous function is one in which arbitrarily small changes in the input produce arbitrarily small changes in the output. ... Open circuit can mean:- In electronics, where there is nothing connected to a load and no current can flow. ... For alternate meanings see Short circuit (disambiguation) A short circuit (sometimes known as simply a short) is a fault whereby electricity moves through a circuit in an unintended path, usually due to a connection forming where none was expected. ... There are very few or no other articles that link to this one. ...

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). 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). ...

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:

y₁ = y₀sin(kx − ωt)
and y₂ = y₀sin(kx + ωt)

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

y = y₀sin(kx − ωt) + y₀sin(kx + ωt)

Using a trigonometric identity to simplify,

y = 2y₀cos(ωt)sin(kx)

where y₀ 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

The hexagonal cloud feature at the north pole of Saturn is thought by most astronomers to be some sort of standing wave pattern.

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. Image File history File links No higher resolution available. ... Image File history File links No higher resolution available. ... Adjectives: Saturnian Atmosphere [3] Scale height: 59. ... A vibration in a string is a wave. ... fdg--220. ... In acoustics and telecommunication, the harmonic of a wave is a component frequency of the signal that is an integral multiple of the fundamental frequency. ...

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. A cavity resonator uses resonance to amplify a wave. ... A cavity resonator uses resonance to amplify a wave. ...

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

This is a list of wave topics, by Wikipedia page. ... A wave is a disturbance that propagates through space or spacetime, transferring energy and momentum and sometimes angular momentum. ... An amphidromic point is a point within a tidal system where the tidal range is almost zero. ... In telecommunication, 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). ... The trumpet is a musical instrument in the brass family. ... The first six longitudinal modes of a plane-parallel cavity. ... Modelocking is a technique in optics by which a laser can be made to produce pulses of light of extremely short duration, on the order of picoseconds (10-12s) or femtoseconds (10-15s). ... A seiche (pronounced saysh) or an underwater wave is a standing wave in a body of water. ... This is a list of communications, computers, electronic circuits, fiberoptics, microelectronics, medical electronics, reliablity, and semiconductors. ... Electrical impedance, or simply impedance, is a measure of opposition to a sinusoidal alternating electric current. ... Federal Standard 1037C, entitled Telecommunications: Glossary of Telecommunication Terms is a United States Federal Standard, issued by the General Services Administration pursuant to the Federal Property and Administrative Services Act of 1949, as amended. ... For other types of mode, see mode. ... To meet Wikipedias quality standards, this article or section may require cleanup. ... The characteristic impedance of a uniform transmission line is the ratio of the amplitudes of a single pair of voltage and current waves propagating along the line in the absence of reflections. ... Hans Jenny created this image during his studies of cymatics. ... Nikola Tesla (1856-1943)[1] was a world-renowned Serbian inventor, physicist, mechanical engineer and electrical engineer. ...

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.
• Java applet of transverse standing wave
• Java applet showing the production of standing wave on a string by adjusting frequency