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Standing waves

There are two ways that we can approach this analysis. If the wire is very long, we can think in terms of a deformation pulse that propagates along thewire passing by our sensors once and only once. This would fall into the category of transient analysis .

On the other hand, if the wire is shorter, we can think in terms of vibrating one end of the wire in such a way that a standing wave will develop on the wire.This is probably the easier of the two approaches to understand because you may have created standing waves on a rope as a child.

What does a standing wave look like?

Once a standing wave is set up on the wire, it will take on an appearance very similar to the sine wave shown in Figure 1 .

Figure 1. A standing wave on a wire.
missing image

Figure 1 represents a snapshot taken at a single instant in time. Obviously the wire doesn't remain in the position shown in Figure 1 for very long. Rather a single point on the wire will move up and down with time with the overallappearance being as shown in Figure 1 . The distance between any two positive peaks is what we would refer to as the wavelength of the standing wave.

Add the sensor output signals

Now consider what would happen if we were to electronically add the electrical outputs produced by the two sensors. The result would depend on thedistance between the sensors relative to the wavelength of the standing wave. For example, if the two sensors were exactly one wavelength apart, the twosensors would move up and down in unison, and the sum of the two signals would be double the signal level produced by either sensor alone. The result would bethe same as if the two sensors were located at the same place on the wire.

A one-half wavelength spacing

On the other hand, if the two sensors were exactly one-half wavelength apart, one would be going up when the other is going down, and the electrical outputfrom one would cancel the electrical output from the other. In space processing terminology, this would be referred to as a null point .

Change the wavelength of the standing wave

Now consider what would happen if you were to leave the two sensors in the same locations as before and do something to the wire to change the wavelengthof the standing wave. The output from the sum of the two sensors would range from zero to maximum as the wavelength relative to the sensor separation variesfrom one-half wavelength to one full wavelength. For a one-half wavelength separation, the output would be zero. For a full wavelength separation,the output would be at its maximum.

A two-element array

We could refer to our two sensors as a two-element array , and we could refer to the output produced by the sum of the two sensors as the responseof the array. We could plot the response versus wavelength. However, in the same sense that it is more common to plot the response of electrical filters versusfrequency (instead of period) , it is probably most common to plot the response of arrays versus wavenumber (instead of wavelength) . Therefore, in this module, we will plot the response of the array versuswavenumber.

Questions & Answers

are nano particles real
Missy Reply
yeah
Joseph
Hello, if I study Physics teacher in bachelor, can I study Nanotechnology in master?
Lale Reply
no can't
Lohitha
where we get a research paper on Nano chemistry....?
Maira Reply
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
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..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
Google
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
revolt
da
Application of nanotechnology in medicine
has a lot of application modern world
Kamaluddeen
yes
narayan
what is variations in raman spectra for nanomaterials
Jyoti Reply
ya I also want to know the raman spectra
Bhagvanji
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.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
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
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Digital signal processing - dsp. OpenStax CNX. Jan 06, 2016 Download for free at https://legacy.cnx.org/content/col11642/1.38
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