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. Vibration refers to mechanical Oscillations about an equilibrium point. The fundamental tone, often referred to simply as the fundamental and abbreviated fo, is the lowest frequency in a harmonic series. An overtone is a natural resonance or vibration frequency of a system A wave is a disturbance that propagates through Space and Time, usually with transference of Energy. 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 travelling in opposite directions. In physics interference is the addition ( superposition) of two or more Waves that result in a new wave pattern In the second case, for waves of equal amplitude travelling in opposing directions, there is on average no net propagation of energy. Amplitude is the magnitude of change in the oscillating variable with each Oscillation, within an oscillating system In Mathematics, an average, or central tendency of a Data set refers to a measure of the "middle" or " expected " value of In the various subfields of Physics, there exist two common usages of the term flux, both with rigorous mathematical frameworks

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. In Meteorology, lee waves, are atmospheric Standing waves. The most common form is mountain waves, which are atmospheric internal Gravity Such waves are often exploited by glider pilots. Gliding is a Recreational activity and competitive Sport in which pilots fly un-powered aircraft known as Gliders or sailplanes

Standing waves and hydraulic jumps also form on fast flowing river rapids and tidal currents such as the Saltstraumen maelstrom. A hydraulic jump is a phenomenon in the science of Hydraulics which is frequently observed in open channel flow such as Rivers and Spillways. 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 Saltstraumen is a sound with a strong tidal current located in Nordland 30 km east of the city of Bodø, Norway. A maelstrom (or malström/malstrøm in the Scandinavian languages) 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. A node is a point along a Standing wave where the wave has minimal Amplitude.

Electric force vector (E) and magnetic force vector (H) of a Standing Wave.

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. 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 Electric current is the flow (movement of Electric charge. The SI unit of electric current is the Ampere. Electrical tension (or voltage after its SI unit, the Volt) is the difference of electrical potential between two points of an electrical In Physics, the field strength of a field is the magnitude of its vector value The effect is a series of nodes (zero displacement) and anti-nodes (maximum displacement) at fixed points along the transmission line. A node is a point along a Standing wave where the wave has minimal Amplitude. Particle displacement or particle amplitude (represented in Mathematics by the lower-case Greek letter &xi) is a Measurement A node is a point along a Standing wave where the wave has minimal Amplitude. Particle displacement or particle amplitude (represented in Mathematics by the lower-case Greek letter &xi) is a Measurement 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. Signal reflection occurs when a signal is transmitted along a transmission medium such as a Copper cable or an Optical fiber, some of the signal power may be reflected Electrical impedance, or simply impedance, describes a measure of opposition to a sinusoidal Alternating current (AC Impedance matching is the electronics design practice of setting the Output impedance ( Z S of a signal source equal to the Input impedance ( e. , discontinuity, such as an open circuit or a short. Short Circuit is a 1986 comedy Science fiction film starring Ally Sheedy and Steve Guttenberg and directed by The failure of the line to transfer power at the standing wave frequency will usually result in attenuation distortion. Attenuation distortion is the Distortion of an Analog signal that occurs during transmission when the Transmission medium does not have a flat

Another example are standing waves in the open ocean formed by waves with the same wave period moving in opposite directions. An ocean (from Greek, ''Okeanos'' (Oceanus) is a major body of saline water, and a principal component of the Hydrosphere. These may form near storm centres, or from reflection of a swell at the shore, and are the source of microbaroms and microseisms. In Acoustics, microbaroms, also known as the " voice of the sea "are a class of atmospheric Infrasonic Waves generated in

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

Mathematical description

The equation of a standing wave is represented as follows:
Two waves with the same frequency, wavelength and amplitude travelling in opposite directions will interfere and produce a 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:

• y₀ is the amplitude of the wave,
• ω (called angular frequency, measured in radians per second) is 2π times the frequency (in hertz),
• k (called the wave number and measured in radians per metre) is 2π divided by the wavelength λ (in metres), and
• x and t are variables for longitudinal position and time, respectively. Amplitude is the magnitude of change in the oscillating variable with each Oscillation, within an oscillating system Do not confuse with Angular velocity In Physics (specifically Mechanics and Electrical engineering) angular frequency The radian is a unit of plane Angle, equal to 180/ π degrees, or about 57 Frequency is a measure of the number of occurrences of a repeating event per unit Time. The hertz (symbol Hz) is a measure of Frequency, informally defined as the number of events occurring per Second. Wavenumber in most physical sciences is a Wave property inversely related to Wavelength, having SI units of reciprocal meters In Physics wavelength is the distance between repeating units of a propagating Wave of a given Frequency.

So the resultant wave y equation will be the sum of y₁ and y₂:

Using a trigonometric identity to simplify, the standing wave is described by:

At nodes x = 0, λ/2, λ, 3λ/2 ··· etc. In Mathematics, trigonometric identities are equalities that involve Trigonometric functions that are true for every single value of the occurring variables A node is a point along a Standing wave where the wave has minimal Amplitude. whereas at anti-nodes x = λ/4, 3λ/4, 5λ/4 ··· etc. A node is a point along a Standing wave where the wave has minimal Amplitude. The distance between two conjugative nodes or anti-nodes is λ/2.

Physical waves

The hexagonal cloud feature at the north pole of Saturn is thought 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. A Vibration in a string is a Wave. Usually a vibrating string produces a Sound whose Frequency in most cases is constant The fundamental tone, often referred to simply as the fundamental and abbreviated fo, is the lowest frequency in a harmonic series. In Acoustics and Telecommunication, the harmonic of a Wave is a component Frequency of the signal that is an Integer Nodes occur at fixed ends and anti-nodes 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. An optical cavity or optical resonator is an arrangement of Mirrors that forms a Standing wave Cavity resonator for Light waves Optical In an optical cavity, the light wave from one end is made to reflect from the other. An optical cavity or optical resonator is an arrangement of Mirrors that forms a Standing wave Cavity resonator for Light waves Optical The transmitted and reflected waves superpose, and form a standing-wave pattern.

See also

• List of wave topics:

Amphidromic point, Clapotis, Longitudinal mode, Modelocking, Seiche, Trumpet, Voltage standing wave ratio, Wave

• List of electronics topics:

Cavity resonator, Characteristic impedance, Cymatics, Impedance, Federal Standard 1037C, Normal mode

External links

• Vibrations and Waves - a chapter from an online textbook
• Standing Waves experiment Shows how the point moves with frequency change. This is a list of Wave topics. 0&ndash9 21 cm line A Abbe prism An amphidromic point is a point within a tidal system where the Tidal range is almost zero In Hydrodynamics, the clapotis (from "lapping of water" is a non-breaking Standing wave pattern caused for example by the reflection of a traveling surface A longitudinal mode of a Resonant cavity is a particular Standing wave pattern formed by Waves confined in the cavity Mode-locking 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 Seiche is also a French term for a type of Cuttlefish (Sepiida In Telecommunications standing wave ratio ( SWR) is the Ratio of the Amplitude of a partial Standing wave at an antinode (maximum A wave is a disturbance that propagates through Space and Time, usually with transference of Energy. Alphabetization has been neglected in some parts of this article (the "b" section in particular A resonator is a device or system that exhibits Resonance or resonant behavior that is it naturally oscillates at some frequencies, called its resonance The characteristic impedance or surge impedance of a uniform Transmission line, usually written Z_0 is the ratio of the amplitudes of a single Cymatics is the study of Wave phenomena It is typically associated with the physical patterns produced through the interaction of Sound Electrical impedance, or simply impedance, describes a measure of opposition to a sinusoidal Alternating current (AC Federal Standard 1037C, entitled Telecommunications Glossary of Telecommunication Terms is a United States Federal Standard issued by the General Services Administration A normal mode of an oscillating system is a pattern of motion in which all parts of the system move sinusoidally with the same frequency
• 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