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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

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
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
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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?
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What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
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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
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What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
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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
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Introduction about quantum dots in nanotechnology
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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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