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Standing wave

 
Standing Wave

 
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Standing wave
 
 
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A standing wave, also known as a stationary wave, is a wave
Wave

A wave is a disturbance that propagates through space and time, usually with transference of energy. While a mechanical wave exists in a medium , waves of electromagnetic radiation can travel through vacuum, that is, without a medium....
 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
Interference

In physics, interference is the addition of two or more waves that result in a new wave pattern.Interference usually refers to the interaction of waves which are correlated or Coherence with each other, either because they come from the same source or because they have the same or nearly the same frequency....
 between two waves traveling in opposite directions. In the second case, for waves of equal amplitude
Amplitude

Amplitude is the magnitude of change in the oscillating variable, with each oscillation, within an oscillating system. For instance, sound waves are oscillations in atmospheric pressure and their amplitudes are proportional to the change in pressure during one oscillation....
 traveling in opposing directions, there is on average
Average

In mathematics, an average, or central tendency of a data set refers to a measure of the "middle" or "Expected value" value of the data set....
 no net propagation of energy
Flux

In the various subfields of physics, there exist two common usages of the term flux, both with rigorous mathematical frameworks.*In the study of transport phenomena , flux is defined as the amount that flows through a unit area per unit time....
.

Standing waves in resonator
Resonator

A resonator is a device or system that exhibits resonance or resonant behavior, that is, it naturally Oscillation at some frequency, called its Resonance frequency, with greater amplitude than at others....
s are one cause of the phenomenon called resonance
Resonance

In physics, resonance is the tendency of a system to oscillate at maximum amplitude at certain Frequency, known as the system's resonance frequencies ....
.
Moving medium
As an example of the first type, under certain meteorological conditions standing waves form in the atmosphere in the lee
Lee waves

In meteorology, lee waves, are Earth's atmosphere standing waves. The most common form is mountain waves, which are atmospheric internal gravity waves....
 of mountain ranges.






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Encyclopedia


A standing wave, also known as a stationary wave, is a wave
Wave

A wave is a disturbance that propagates through space and time, usually with transference of energy. While a mechanical wave exists in a medium , waves of electromagnetic radiation can travel through vacuum, that is, without a medium....
 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
Interference

In physics, interference is the addition of two or more waves that result in a new wave pattern.Interference usually refers to the interaction of waves which are correlated or Coherence with each other, either because they come from the same source or because they have the same or nearly the same frequency....
 between two waves traveling in opposite directions. In the second case, for waves of equal amplitude
Amplitude

Amplitude is the magnitude of change in the oscillating variable, with each oscillation, within an oscillating system. For instance, sound waves are oscillations in atmospheric pressure and their amplitudes are proportional to the change in pressure during one oscillation....
 traveling in opposing directions, there is on average
Average

In mathematics, an average, or central tendency of a data set refers to a measure of the "middle" or "Expected value" value of the data set....
 no net propagation of energy
Flux

In the various subfields of physics, there exist two common usages of the term flux, both with rigorous mathematical frameworks.*In the study of transport phenomena , flux is defined as the amount that flows through a unit area per unit time....
.

Standing waves in resonator
Resonator

A resonator is a device or system that exhibits resonance or resonant behavior, that is, it naturally Oscillation at some frequency, called its Resonance frequency, with greater amplitude than at others....
s are one cause of the phenomenon called resonance
Resonance

In physics, resonance is the tendency of a system to oscillate at maximum amplitude at certain Frequency, known as the system's resonance frequencies ....
.

Moving medium


As an example of the first type, under certain meteorological conditions standing waves form in the atmosphere in the lee
Lee waves

In meteorology, lee waves, are Earth's atmosphere standing waves. The most common form is mountain waves, which are atmospheric internal gravity waves....
 of mountain ranges. Such waves are often exploited by glider pilots
Gliding

Gliding refers to the descending flight of heavier-than-air craft, principally gliders s, hang gliders and paragliders. Technically, gliders, hang-gliders and paragliders are just different styles of glider used to pursue gliding and soaring for recreation, in the same way that sailboats and windsurfers share the lake and the wind....
.

Standing waves and hydraulic jump
Hydraulic jump

A hydraulic jump is a phenomenon in the science of hydraulics which is frequently observed in open channel flow such as rivers and spillways. When liquid at high velocity discharges into a zone of lower velocity, a rather abrupt rise occurs in the liquid surface....
s also form on fast flowing river rapids
Rapid

File:Rapids.jpgFile:!downstream river1.jpgA rapid is a section of a river where the river bed has a relatively steep stream gradient causing an increase in water [velocity and turbulence....
 and tidal currents such as the Saltstraumen
Saltstraumen

Saltstraumen is a Sound with a strong Tide located in Nordland 30 km east of the city of Bod?, Norway. The narrow channel connects the outer Saltfjord with its extension, the large Skjerstadfjord....
 maelstrom
Maelstrom

A maelstrom is a very powerful whirlpool; a large, swirling body of water. A free vortex, it has considerable downdraft. The Nordic word was introduced into English by Edgar Allan Poe in his story "A Descent into the Maelstr?m" ....
.

Opposing waves


Standing Wave
As an example of the second type, a standing wave in a transmission line
Transmission line

A transmission line is the material Transmission medium or structure that forms all or part of a Course from one place to another for directing the transmission of energy, such as electromagnetic waves or acoustic waves, as well as electric power transmission....
 is a wave in which the distribution of current, voltage
Voltage

Electrical tension is the potential difference between two points of an electrical or electronic circuit, expressed in volts. It is the measurement of the potential for an electric field to cause an electric current in an electrical conductor....
, or field strength
Field strength

In physics, the field strength of a field is the magnitude of its vector value.In theoretical physics, field strength is another name for the curvature form....
 is formed by the superposition
Superposition

The term superposition can have several meanings:* the superposition principle in physics, mathematics, and engineering, describes the overlapping of waves and can show how either constructive, or destructive Interference will occur....
 of two waves of the same frequency
Frequency

Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency....
 propagating in opposite directions. The effect is a series of node
Node (physics)

A node is a point along a standing wave where the wave has minimal amplitude. For instance, in a vibrating guitar string, the ends of the string are nodes....
s (zero displacement
Particle displacement

Particle displacement or particle amplitude is a measurement of distance of the movement of a particle in a medium as it transmits a wave....
) and anti-nodes (maximum displacement
Particle displacement

Particle displacement or particle amplitude is a measurement of distance of the movement of a particle in a medium as it transmits a wave....
) 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
Electrical impedance

Electrical impedance, or simply impedance, describes a measure of opposition to a sinusoidal alternating current . Electrical impedance extends the concept of Electrical resistance to AC circuits, describing not only the relative amplitudes of the voltage and Electric current, but also the relative Phase ....
 mismatch, i.e., discontinuity
Discontinuity

Discontinuity can be:*Discontinuity , a property of a mathematical functionDiscontinuity may also refer to:*A break in continuity , in literature...
, such as an open circuit
Open circuit

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...
 or a short
Short circuit

A short circuit in an electrical circuit that allows a Electric current along a different path from the one intended.The electrical opposite of a short circuit is an "open circuit", which is an infinite resistance between two nodes....
. The failure of the line to transfer power at the standing wave frequency will usually result in attenuation distortion
Attenuation Distortion

Attenuation distortion 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....
.

Another example is standing waves in the open ocean
Ocean

An ocean is a major body of Seawater, and a principal component of the hydrosphere. Approximately 71% of the Earth's surface is covered by ocean, a World Ocean that is customarily divided into several principal oceans and smaller seas....
 formed by waves with the same wave period moving in opposite directions. These may form near storm centres, or from reflection of a swell at the shore, and are the source of microbarom
Microbarom

In acoustics, microbaroms, also known as the "voice of the sea",are a class of Earth's atmosphere infrasonic waves generated in marine storms...
s and microseism
Microseism

A microseism is defined as a faint earth tremor caused by natural phenomena, such as winds and ocean waves. Thus a microseism is a small and long-continuing oscillation of the ground....
s.

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 traveling wave. The degree to which the wave resembles either a pure standing wave or a pure traveling wave is measured by the standing wave ratio
Standing wave ratio

In telecommunications, standing wave ratio is the ratio of the amplitude of a partial standing wave at an antinode to the amplitude at an adjacent node , in an electrical transmission line....
 (SWR).

Mathematical description

In one dimension, two waves with the same frequency, wavelength and amplitude traveling in opposite directions will interfere and produce a standing wave or stationary wave. For example: a harmonic wave traveling 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
    Amplitude

    Amplitude is the magnitude of change in the oscillating variable, with each oscillation, within an oscillating system. For instance, sound waves are oscillations in atmospheric pressure and their amplitudes are proportional to the change in pressure during one oscillation....
     of the wave,
  • ? (called angular frequency
    Angular frequency

    In physics , angular frequency ? is a scalar measure of rotation rate. Angular frequency is the magnitude of the vector quantity angular velocity....
    , measured in radian
    Radian

    The radian is a unit of plane angle, equal to 180/pi Degree , or about 57.2958 degrees, or about 57?17'45?. It is the standard unit of angular measurement in all areas of mathematics beyond the elementary level....
    s per second    ) is 2p times the frequency
    Frequency

    Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency....
     (in hertz
    Hertz

    The hertz is a measure of frequency per unit of time, or the number of list of cycles per second. It is the SI base unit of frequency in the International System of Units , and is used worldwide in both general-purpose and scientific contexts....
    ),
  • k (called the wave number and measured in radians per metre) is 2p divided by the wavelength
    Wavelength

    In physics, wavelength is the distance between repeating units of a propagating wave of a given frequency. It is commonly designated by the Greek language letter lambda ....
     ? (in metres), and
  • x and t are variables for longitudinal position and time, respectively.


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:

This describes a wave that oscillates in time, but has a spatial dependence that is stationary: sin(kx). At locations x = 0, ?/2, ?, 3?/2, ... called the node
Node (physics)

A node is a point along a standing wave where the wave has minimal amplitude. For instance, in a vibrating guitar string, the ends of the string are nodes....
s the amplitude is always zero, whereas at locations x = ?/4, 3?/4, 5?/4, ... called the anti-nodes, the amplitude is maximum. The distance between two conjugative nodes or anti-nodes is ?/2.

Standing waves can also occur in more than one dimension, such as in a resonator
Resonator

A resonator is a device or system that exhibits resonance or resonant behavior, that is, it naturally Oscillation at some frequency, called its Resonance frequency, with greater amplitude than at others....
. The illustration on the right shows a standing wave on a disk.

Physical waves

Standing waves are also observed in physical media such as strings and columns of air. Any waves traveling 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
Vibrating string

A vibration in a strings is a wave. Usually a 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....
 or air column's natural frequency, a standing wave is created, allowing harmonics to be identified. Nodes occur at fixed ends and anti-nodes at open ends. If fixed at only one end, only odd-numbered harmonics are available. At the open end of a pipe the anti-node will not be exactly at the end as it is altered by its contact with the air and so end correction
End correction

In physics, end correction is the anomal difference between the frequency of a tuning fork and the corresponding sound waves inside of a tube. It is caused because generally there is air between the fork and the pipe end, causing the air column to vibrate a short distance beyond the edge of the tube....
 is used to place it exactly.

Optical waves

Standing waves are also observed in optical media such as optical wave guides, optical cavities
Optical cavity

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....
, 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


Amphidromic point
Amphidromic point

An amphidromic point is a point within a tidal system where the tidal range is almost zero.Amphidromic points occur because of the coriolis effect and interference within oceanic basins, seas and Headlands and bayss creating a wave pattern ? called an amphidromic system ? which rotates around the amphidromic point....
, Clapotis
Clapotis

In hydrodynamics, the clapotis is a non-breaking standing wave pattern, caused for example, by the reflection of a traveling surface wave train from a near vertical shoreline like a Breakwater , seawall or steep cliff....
, Longitudinal mode
Longitudinal mode

A longitudinal mode of a resonant cavity is a particular standing wave pattern formed by waves confined in the cavity. The longitudinal modes correspond to the wavelengths of the wave which are reinforced by constructive interference after many reflections from the cavity's reflecting surfaces....
, Modelocking
Modelocking

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 or femtoseconds ....
, Seiche
Seiche

A seiche is a standing wave in an enclosed or partially enclosed body of water. Seiches and seiche-related phenomena have been observed on lakes, Reservoir s, swimming pools, bays and seas....
, Trumpet
Trumpet

The trumpet is a musical instrument with the highest Register in the brass instrument family. Trumpets are among the oldest musical instruments, dating back to at least 1500 BC....
, Voltage standing wave ratio, Wave
Wave

A wave is a disturbance that propagates through space and time, usually with transference of energy. While a mechanical wave exists in a medium , waves of electromagnetic radiation can travel through vacuum, that is, without a medium....
  • List of electronics topics
    List of electronics topics

    This is a list of communications, computers, electronic circuits, fiberoptics, microelectronics, medical electronics, reliability, and semiconductors....
    :
Cavity resonator, Characteristic impedance
Characteristic impedance

The characteristic impedance or surge impedance of a uniform transmission line, usually written , is the ratio of the amplitudes of a single pair of voltage and current waves propagating along the line in the absence of reflections....
, Cymatics
Cymatics

Cymatics is the study of wave phenomena. It is typically associated with the physical patterns produced through the interaction of sound waves in a medium....
, Impedance
Electrical impedance

Electrical impedance, or simply impedance, describes a measure of opposition to a sinusoidal alternating current . Electrical impedance extends the concept of Electrical resistance to AC circuits, describing not only the relative amplitudes of the voltage and Electric current, but also the relative Phase ....
, Federal Standard 1037C
Federal Standard 1037C

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....
, Normal mode
Normal mode

A normal mode of an oscillation is a pattern of motion in which all parts of the system move sinusoidally with the same frequency. The frequencies of the normal modes of a system are known as its natural frequencies or resonant frequencies....


External links

  • - a chapter from an online textbook
  • Shows how the point moves with frequency change.
  • of standing waves on a vibrating string.