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1 2 λ + 1 2 ( 1 2 λ ) = L 2 4 λ + 1 4 λ = L 3 4 λ = L λ = 4 3 L

Case 3 : In this case both ends have to be nodes. This means that the length ofthe tube is one half wavelength: So we can equate the two and solve for the wavelength:

1 2 λ = L λ = 2 L
If you ever calculate a longer wavelength for more nodes you have made a mistake. Remember to check if your answers make sense!

Three nodes

To see the complete pattern for all cases we need to check what the next step for case 3 is when we have an additional node. Below is the diagram for the casewhere n = 3 .

Case 1 : Both ends are open and so they must be anti-nodes. We can have threenodes inside the tube only if we have two anti-nodes contained inside the tube and one on each end. This means we have 4 anti-nodes in thetube. The distance between any two anti-nodes is half a wavelength. This means there is half wavelength between every adjacent pairof anti-nodes. We count how many gaps there are between adjacent anti-nodes to determine how many half wavelengths there are and equate this to the length of the tube L and then solve for λ .

3 ( 1 2 λ ) = L λ = 2 3 L

Case 2 : We want to have three nodes inside the tube. The left end must be anode and the right end must be an anti-node, so there will be two nodes between the ends of the tube. Again we can count the number ofdistances between adjacent nodes or anti-nodes, together these add up to the length of the tube. Remember that the distance between the node and anadjacent anti-node is only half the distance between adjacent nodes. So starting from the left end we count 3 nodes, so 2 half wavelength intervals and then only anode to anti-node distance:

2 ( 1 2 λ ) + 1 2 ( 1 2 λ ) = L λ + 1 4 λ = L 5 4 λ = L λ = 4 5 L

Case 3 : In this case both ends have to be nodes. With one node in between there aretwo sets of adjacent nodes. This means that the length of the tube consists of two half wavelength sections:

2 ( 1 2 λ ) = L λ = L

Superposition and interference

If two waves meet interesting things can happen. Waves are basically collective motion of particles. So when two waves meet they both tryto impose their collective motion on the particles. This can have quite different results.

If two identical (same wavelength, amplitude and frequency) waves are both trying to form a peak then they are able to achieve the sum oftheir efforts. The resulting motion will be a peak which has a height which is the sum of the heights of the two waves. If two waves areboth trying to form a trough in the same place then a deeper trough is formed, the depth of which is the sum of the depths of the twowaves. Now in this case, the two waves have been trying to do the same thing, and so add together constructively. This is called constructive interference .

If one wave is trying to form a peak and the other is trying to form a trough, then they are competing to do different things. Inthis case, they can cancel out. The amplitude of the resulting wave will depend on the amplitudes of the two waves that are interfering. If the depth ofthe trough is the same as the height of the peak nothing will happen. If the height of the peak is bigger than the depth of thetrough, a smaller peak will appear. And if the trough is deeper then a less deep trough will appear. This is destructive interference .

Questions & Answers

where we get a research paper on Nano chemistry....?
Maira Reply
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
ya I also want to know the raman spectra
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
Nasa has use it in the 60's, copper as water purification in the moon travel.
nanocopper obvius
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
analytical skills graphene is prepared to kill any type viruses .
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
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.
Draw a frame of reference with house A as the origin and write down the positions of houses B, C, D and E.
jason Reply

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Source:  OpenStax, Physics - grade 10 [caps 2011]. OpenStax CNX. Jun 14, 2011 Download for free at http://cnx.org/content/col11298/1.3
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