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Eventually the picture looks like the complete reflection through the x -axis of what we started with:

Then all the points begin to move back. Each point on the line is oscillating up and down with a different amplitude.

If we look at the overall result, we get a standing wave.

A standing wave

If we superimpose the two cases where the peaks were at a maximum and the case where the same waves were at a minimum we can see thelines that the points oscillate between. We call this the envelope of the standing wave as it contains all the oscillations of the individual points.To make the concept of the envelope clearer let us draw arrows describing the motion of points along the line.

Every point in the medium containing a standing wave oscillates up and down and the amplitude of the oscillations depends on thelocation of the point. It is convenient to draw the envelope for the oscillations to describe the motion. We cannot draw the up and downarrows for every single point!

Interesting fact

Standing waves can be a problem in for example indoor concerts where the dimensions of the concert venue coincide with particular wavelengths. Standing waves can appear as `feedback', which would occur if the standing wave was picked up by the microphones on stage and amplified.

Nodes and anti-nodes

A node is a point on a wave where no displacement takes place at any time. In a standing wave, a node is a place where two waves cancel out completely as the two waves destructively interfere in thesame place. A fixed end of a rope is a node. An anti-node is a point on a wave where maximum displacement takes place. In a standingwave, an anti-node is a place where the two waves constructively interfere. Anti-nodes occur midway between nodes. A free end of a rope is an anti-node.


A node is a point on a standing wave where no displacement takes place at any time. A fixed end of a rope is a node.


An anti-node is a point on standing a wave where maximum displacement takes place. A free end of a rope is an anti-node.

The distance between two anti-nodes is only 1 2 λ because it is the distance from a peak to a trough in one of the waves forming the standing wave. It is the same as the distance between two adjacent nodes. This will be important when we work out the allowed wavelengths in tubes later. We can take this further because half-way between any two anti-nodes is a node. Then the distance from the node to the anti-node is half the distance between two anti-nodes. This is half of half a wavelength which is one quarter of a wavelength, 1 4 λ .

Wavelengths of standing waves with fixed and free ends

There are many applications which make use of the properties of waves and the use of fixed and free ends. Most musical instruments rely onthe basic picture that we have presented to create specific sounds, either through standing pressure waves or standing vibratory waves instrings.

The key is to understand that a standing wave must be created in the medium that is oscillating. There are restrictions as to whatwavelengths can form standing waves in a medium.

Questions & Answers

what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
yes that's correct
I think
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
how nano science is used for hydrophobicity
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
what is differents between GO and RGO?
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Siyavula textbooks: grade 10 physical science. OpenStax CNX. Aug 29, 2011 Download for free at http://cnx.org/content/col11245/1.3
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