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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.

For example, if we consider a rope that can move in a pipe such that it can have

  • both ends free to move (Case 1)
  • one end free and one end fixed (Case 2)
  • both ends fixed (Case 3).

Each of these cases is slightly different because the free or fixed end determines whether a node or anti-node will form when a standingwave is created in the rope. These are the main restrictions when we determine the wavelengths of potential standing waves. These restrictions are known as boundary conditions and must be met.

In the diagram below you can see the three different cases. It is possible to create standing waves with different frequencies andwavelengths as long as the end criteria are met.

The longer the wavelength the less the number of anti-nodes in the standing waves. We cannot have a standing wave with no anti-nodes becausethen there would be no oscillations. We use n to number the anti-nodes. If all of the tubes have a length L and we know the end constraints we can find the wavelength, λ , for a specific number of anti-nodes.

One node

Let's work out the longest wavelength we can have in each tube, i.e. the case for n = 1 .

Case 1 : In the first tube, both ends must be anti-nodes, so we must place onenode in the middle of the tube. We know the distance from one anti-node to another is 1 2 λ and we also know this distance is L. So we can equate the two and solve for the wavelength:

1 2 λ = L λ = 2 L

Case 2 : In the second tube, one end must be a node and the other must be ananti-node. Since we are looking at the case with one node, we are forced to have it at the end. We know the distance from onenode to another is 1 2 λ but we only have half this distance contained in the tube. So :

1 2 1 2 λ = L λ = 4 L

Case 3 : Here both ends are closed and so we must have two nodes so it isimpossible to construct a case with only one node.

Two nodes

Next we determine which wavelengths could be formed if we had two nodes. Remember that we are dividing the tube up into smaller andsmaller segments by having more nodes so we expect the wavelengths to get shorter.

Case 1 : Both ends are open and so they must be anti-nodes. We can have twonodes inside the tube only if we have one anti-node contained inside the tube and one on each end. This means we have 3 anti-nodes in thetube. The distance between any two anti-nodes is half a wavelength. This means there is half wavelength between the left sideand the middle and another half wavelength between the middle and the right side so there must be one wavelength inside the tube. The safestthing to do is work out how many half wavelengths there are and equatethis to the length of the tube L and then solve for λ .

2 ( 1 2 λ ) = L λ = L

Case 2 : We want to have two nodes inside the tube. The left end must be anode and the right end must be an anti-node. We can have one node inside the tube as drawn above. Again we can count the number ofdistances between adjacent nodes or anti-nodes. If we start from the left end we have one half wavelength between the end and the nodeinside the tube. The distance from the node inside the tube to the right end which is an anti-node is half of the distance to anothernode. So it is half of half a wavelength. Together these add up to the length of the tube:

Questions & Answers

how do they get the third part x = (32)5/4
kinnecy Reply
can someone help me with some logarithmic and exponential equations.
Jeffrey Reply
sure. what is your question?
ninjadapaul
20/(×-6^2)
Salomon
okay, so you have 6 raised to the power of 2. what is that part of your answer
ninjadapaul
I don't understand what the A with approx sign and the boxed x mean
ninjadapaul
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
Salomon
I'm not sure why it wrote it the other way
Salomon
I got X =-6
Salomon
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
ninjadapaul
oops. ignore that.
ninjadapaul
so you not have an equal sign anywhere in the original equation?
ninjadapaul
Commplementary angles
Idrissa Reply
hello
Sherica
im all ears I need to learn
Sherica
right! what he said ⤴⤴⤴
Tamia
hii
Uday
what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
Kevin Reply
a perfect square v²+2v+_
Dearan Reply
kkk nice
Abdirahman Reply
algebra 2 Inequalities:If equation 2 = 0 it is an open set?
Kim Reply
or infinite solutions?
Kim
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Al
y=10×
Embra Reply
if |A| not equal to 0 and order of A is n prove that adj (adj A = |A|
Nancy Reply
rolling four fair dice and getting an even number an all four dice
ramon Reply
Kristine 2*2*2=8
Bridget Reply
Differences Between Laspeyres and Paasche Indices
Emedobi Reply
No. 7x -4y is simplified from 4x + (3y + 3x) -7y
Mary Reply
is it 3×y ?
Joan Reply
J, combine like terms 7x-4y
Bridget Reply
how do you translate this in Algebraic Expressions
linda Reply
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
Crystal Reply
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
Chris Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
China
Cied
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
AMJAD
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
AMJAD
what is system testing
AMJAD
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
Hello
Uday
I'm interested in Nanotube
Uday
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
Prasenjit
can nanotechnology change the direction of the face of the world
Prasenjit Reply
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
Ali Reply
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
bamidele Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit 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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