digplanet beta 1: Athena
Share digplanet:

Agriculture

Applied sciences

Arts

Belief

Business

Chronology

Culture

Education

Environment

Geography

Health

History

Humanities

Language

Law

Life

Mathematics

Nature

People

Politics

Science

Society

Technology

For other uses, see Hydraulic jump.

In physics, a standing wave – also known as a stationary wave – is a wave that remains in a constant position.

Two opposing waves combine to form a standing wave.

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. In the second case, for waves of equal amplitude traveling in opposing directions, there is on average no net propagation of energy.

In a resonator, standing waves occur during the phenomenon known as resonance.

Moving medium[edit]

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. Many standing river waves are popular river surfing breaks.

Opposing waves[edit]

Standing 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 of the same frequency 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.[1] 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 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 (SWR).[2]

Another example is standing waves in the open ocean 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 microbaroms and microseisms.

Mathematical description[edit]

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 wave traveling to the right along a taut string and hitting the end will reflect back in the other direction along the string, and the two waves will superpose to produce a standing wave. The reflective wave has to have the same amplitude and frequency as the incoming wave.

If the string is held at both ends, forcing zero movement at the ends, the ends become zeroes or nodes of the wave. The length of the string then becomes a measure of which waves the string will entertain: the longest wavelength is called the fundamental. Half a wavelength of the fundamental fits on the string. Shorter wavelengths also can be supported as long as multiples of half a wavelength fit on the string. The frequencies of these waves all are multiples of the fundamental, and are called harmonics or overtones. For example, a guitar player can select an overtone by putting a finger on a string to force a node at the proper position between the ends of the string, suppressing all harmonics that do not share this node.

Harmonic waves travelling in opposite directions can be represented by the equations below:


y_1\; =\; y_0\, \sin(kx - \omega t)\,

and


y_2\; =\; y_0\, \sin(kx +\omega t)\,

where:

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


y\; =\; y_0\, \sin(kx - \omega t)\; +\; y_0\, \sin(kx + \omega t).\,

Using the trigonometric sum-to-product identity for 'sin(u) + sin(v)' to simplify:


y\; =\; 2\, y_0\, \cos(\omega t)\; \sin(kx).\,

This describes a wave that oscillates in time, but has a spatial dependence that is stationary: sin(kx). At locations x = 0, λ/2, λ, 3λ/2, ... called the nodes the amplitude is always zero, whereas at locations x = λ/4, 3λ/4, 5λ/4, ... called the anti-nodes, the amplitude is maximum. The distance between two conjugative nodes or anti-nodes is λ/2.

Standing waves can also occur in two- or three-dimensional resonators. With standing waves on two-dimensional membranes such as drumheads, illustrated in the animations above, the nodes become nodal lines, lines on the surface at which there is no movement, that separate regions vibrating with opposite phase. These nodal line patterns are called Chladni figures. In three-dimensional resonators, such as musical instrument sound boxes and microwave cavity resonators, there are nodal surfaces.

Examples[edit]

One easy to understand example of standing waves is two people shaking either end of a jump rope. If they shake in sync the rope can form a regular pattern of waves oscillating up and down, with stationary points along the rope where the rope is almost still (nodes) and points where the arc of the rope is maximum (antinodes)

Sound waves[edit]

The hexagonal cloud feature at the north pole of Saturn was initially thought to be standing Rossby waves.[3] This explanation has recently been disputed though.[4]

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 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 is used to place it exactly. The density of a string will affect the frequency at which harmonics will be produced; the greater the density the lower the frequency needs to be to produce a standing wave of the same harmonic.

Light[edit]

Standing waves are also observed in optical media such as optical wave guides, optical cavities, etc. Lasers use optical cavities in the form of a pair of facing mirrors. The gain medium in the cavity (such as a crystal) emits light coherently, exciting standing waves of light in the cavity. The wavelength of light is very short (in the range of nanometers, 10-9 m) so the standing waves are microscopic in size. One use for standing light waves is to measure small distances, using optical flats.

Mechanical waves[edit]

Standing waves can be mechanically induced into solid medium using resonance. One easy way to understand example is two people shaking either end of a jump rope. If they shake in sync, the rope will form a regular pattern with nodes and antinodes and appear to be stationary, hence the name standing wave. Similarly a cantilever beam can have a standing wave imposed on it by applying a base excitation. In this case the free end moves the greatest distance laterally compared to any location along the beam. Such a device can be used as a sensor to track changes in frequency or phase of the resonance of the fiber. One application is as a measurement device for dimensional metrology.[5][6]

Seismic waves[edit]

Standing surface waves on the Earth are observed as free oscillations of the Earth.

Faraday waves[edit]

The Faraday wave is a non-linear standing wave at the air-liquid interface induced by hydrodynamic instability. It can be used as a liquid-based template to assemble microscale materials.[7]

See also[edit]

Amphidromic point, Clapotis, Longitudinal mode, Modelocking, Metachronal rhythm. Resonant room modes, Seiche, Trumpet, Voltage standing wave ratio, Wave, Kundt's tube
Cavity resonator, Characteristic impedance, Cymatics, Impedance, Normal mode

References and notes[edit]

  1. ^  This article incorporates public domain material from the General Services Administration document "Federal Standard 1037C".
  2. ^ Blackstock, David T. (2000), Fundamentals of Physical Acoustics, Wiley–IEEE, ISBN 0-471-31979-1 , 568 pages. See page 141.
  3. ^ A Wave Dynamical Interpretation of Saturn's Polar Region, M. Allison, D. A. Godfrey, R. F. Beebe, Science vol. 247, pg. 1061 (1990)
  4. ^ A laboratory model of Saturn’s North Polar Hexagon, A. C. Barbosa Aguiar, P. L. Read, R. D. Wordsworth, T. Salter, Y. H. Yamazaki, Icarus, vol. 206 (2009)
  5. ^ M.B. Bauza, R.J Hocken, S.T Smith, S.C Woody, (2005), The development of a virtual probe tip with application to high aspect ratio microscale features, Rev. Sci Instrum, 76 (9) 095112  .
  6. ^ http://www.insitutec.com
  7. ^ P. Chen, Z. Luo, S. Guven, S. Tasoglu, A. Weng, A. V. Ganesan, U. Demirci, Advanced Materials 2014, 10.1002/adma.201402079. http://onlinelibrary.wiley.com/doi/10.1002/adma.201402079/abstract

External links[edit]


Original courtesy of Wikipedia: http://en.wikipedia.org/wiki/Standing_wave — Please support Wikipedia.
This page uses Creative Commons Licensed content from Wikipedia. A portion of the proceeds from advertising on Digplanet goes to supporting Wikipedia.
1000000 videos foundNext > 

Standing Waves Part I: Demonstration

Demonstration of standing waves on a string. How the standing waves are generated, harmonics and more is explained here. By James Dann for ck12.org CC-BY-NC-SA.

Making standing waves

A standing wave is made by sending a wave group down the tank against a fixed wall. The reflected wave will superimpose upon the incident waves doubling the ...

Waimea River Standing Wave Surf Session

Surfers dig a channel thru the sand, releasing the Waimea river water trapped behind the beach. They surf the resulting standing waves for several hours.

Standing Waves Generated by String Vibration

Standing Waves Generated by machine-controlled String Vibration.

Doc Physics - Standing wave harmonics on guitar strings (and pianos, banjos, and harps, I guess)

Why do strings make the sounds they do, yo? Various harmonics are investigated and justified.

Standing Waves Physics Lesson

http://www.physicseh.com/ Free simple easy to follow videos all organized on our website.

Pyro Board: 2D Rubens' Tube!

Standing waves of fire! Check out Audible: http://bit.ly/AudibleVe Fysikshow: http://bit.ly/Fysikshow - I'm hosting Michio Kaku in Melbourne ONLY: http://bit...

Curl Curl Lagoon Standing Wave

http://www.vimeo.com/tylerb http://www.vimeo.com/tylerb http://www.vimeo.com/tylerb http://www.vimeo.com/tylerb Curl Curl Lagoon Standing Wave, Young local s...

EPIC RIVER SURFING!! Standing Wave In Switzerland 2014

New video MONDAY!! Check out the original creators channel!! : https://www.youtube.com/channel/UCZsV3KwFgcFQtskR-BtEL7w Riders: Cyril Inauen, Roland Hauser F...

Standing Wave Generator

Visualize wave properties of electrons, including resonance, nodes, and antinodes. This video is part of the Flinn Scientific Best Practices for Teaching Che...

1000000 videos foundNext > 

53 news items

Fars News Agency

News-Medical.net
Tue, 26 Aug 2014 23:45:00 -0700

When the two waves meet, they combine to form a standing wave (a wave that remains in constant position). This wave produces a pressure node, or line of low pressure, running parallel to the direction of cell flow. Cells that encounter this node are ...
 
Times Record
Mon, 25 Aug 2014 07:15:00 -0700

12 special election to continue of a 1 percent city sales tax, Balletine plans to add some new attractions, such as a standing wave machine for surfing or boogie boarding, to help keep Alma's water park competitive, he said. For Ballentine, parks and ...
 
Business Weekly
Tue, 26 Aug 2014 05:45:00 -0700

The actuation of the piezoneedle generates a standing wave that ejects the fluid droplets from the nozzle. Offering maximum flexibility at much lower costs, piezoneedle arrays can be engineered in a wide range of configurations for industrial use and ...
 
Nashua Telegraph
Thu, 21 Aug 2014 06:18:45 -0700

American Wave Machines' SurfStream technology generates natural-feeling standing waves. The SurfStream at Surf's Up is the world's largest standing wave machine, with a 32-foot channel that can produce 2- to 6-foot waves, including barreling waves that ...
 
Overclockers Club
Tue, 26 Aug 2014 15:41:15 -0700

Instead of relying on chemical tags or strong mechanical forces, this method utilizes sound waves to gently guide cells. By using two acoustic transducers on either side of a microchannel, a standing wave can be made with a pressure node parallel to ...

The Independent

The Independent
Mon, 11 Aug 2014 12:02:11 -0700

... in the Arctic may be contributing to the appearance of wide north-south swings in the high-altitude winds flowing globally west to east around the polar region, which can become stuck and amplified in a quasi-stationary pattern known as a “standing ...

Muhlenberg College Athletics

Muhlenberg College Athletics
Tue, 05 Aug 2014 10:48:45 -0700

At the end of the park was a standing wave where surfers lined up and took turns one by one while spectators watched and took pictures. After the bike tour we had a couple of hours to get lunch on our own. In the middle of the city is a large market ...
 
ScienceAlert
Fri, 01 Aug 2014 21:34:55 -0700

This sort of 'trapped' wave is called a standing wave and they are exactly the kind of wave you see when you wiggle a skipping rope from either end and form a single pattern with peaks (where the rope is at the highest point) and nodes (where the rope ...
Loading

Oops, we seem to be having trouble contacting Twitter

Talk About Standing wave

You can talk about Standing wave with people all over the world in our discussions.

Support Wikipedia

A portion of the proceeds from advertising on Digplanet goes to supporting Wikipedia. Please add your support for Wikipedia!