# Standing Wave Research Materials

This page contains a list of user images about Standing Wave which are relevant to the point and besides images, you can also use the tabs in the bottom to browse Standing Wave news, videos, wiki information, tweets, documents and weblinks.

Standing Wave Images

couldn't connect to hostconnect() timed out!
Rihanna - Take A Bow
Music video by Rihanna performing Take A Bow. YouTube view counts pre-VEVO: 66288884. (C) 2008 The Island Def Jam Music Group.
Key & Peele: Substitute Teacher
A substitute teacher from the inner city refuses to be messed with while taking attendance.
FIRETRUCK! (Official Music Video)
BLOOPERS: http://bit.ly/FiretruckBloopers GET THE SONG: http://smo.sh/WMZv7l MILKSHAKE MUSIC VIDEO: http://bit.ly/MilkyMilkshake CHECK OUT THIS FIRETRUCK TEE...
Jimmy Kimmel Live - Celebrities Read Mean Tweets #2 Jimmy Kimmel Live's YouTube channel features clips and recaps of every episode from the late night TV sho...
Draw My Life - Ryan Higa
So i was pretty hesitant to make this video... but after all of your request, here is my Draw My Life video! Check out my 2nd Channel for more vlogs: http://...
Adele - Rolling In The Deep
Music video by Adele performing Rolling In The Deep. (C) 2010 XL Recordings Ltd. #VEVOCertified on July 25, 2011. http://www.vevo.com/certified http://www.yo...
Avril Lavigne - When You're Gone
Music video by Avril Lavigne performing When You're Gone. YouTube view counts pre-VEVO: 696566 (C) 2007 RCA/JIVE Label Group, a unit of Sony Music Entertain...
David Guetta - Just One Last Time ft. Taped Rai
"Just One Last Time" feat. Taped Rai. Available to download on iTunes including remixes of : Tiësto, HARD ROCK SOFA & Deniz Koyu http://smarturl.it/DGJustOne...
PEOPLE ARE AWESOME 2011
YOLO (feat. Adam Levine & Kendrick Lamar)
YOLO is available on iTunes now! http://smarturl.it/lonelyIslandYolo New album coming soon... Check out the awesome band the music in YOLO is sampled from Th...
Most Annoying People On The Internet
Don't be these people. Mapoti See Bloopers and Behind-The-Scenes Here!: http://youtu.be/dfpo7uXwJnM Huge thank you and shout out to Dtrix: http://www.youtube...
Skrillex & Damian "Jr. Gong" Marley - Make It Bun Dem [OFFICIAL VIDEO]
Buy the track here: http://atlr.ec/TZ8yBf Directed by Tony T. Datis.
MACKLEMORE & RYAN LEWIS - CAN'T HOLD US FEAT. RAY DALTON (OFFICIAL MUSIC VIDEO)
Macklemore & Ryan Lewis present the official music video for Can't Hold Us feat. Ray Dalton. Can't Hold Us on iTunes: https://itunes.apple.com/us/album/cant-...

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

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

 Standing waves Standing wave in stationary medium. The red dots represent the wave nodes. A standing wave (black) depicted as the sum of two propagating waves traveling in opposite directions (red and blue). Electric force vector (E) and magnetic force vector (H) of a standing wave. Standing waves in a string — the fundamental mode and the first 6 overtones. A three-dimensional standing wave on a disk; this is the fundamental mode A higher harmonic standing wave on a disk with two nodal lines crossing at the center.

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

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.

## Physical waves

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.

## 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.

## Mechanical waves

Standing waves can be mechanically induced into solid medium using resonance. One easy 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]

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

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
News
Documents
Don't believe everything they write, until confirmed from SOLUTION NINE site.

### What is SOLUTION NINE?

It's a social web research tool
that helps anyone exploring anything.