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Two full peaks but at different locations

If you consider the peaks at the ends of the wavenumber response for the leftmost and center images in Figure 3 to each represent only half a peak (with the other half being off the scale to the left and the right) , all three scenarios have two complete peaks in their wavenumber responses.

(You could think in terms of printing the wavenumber response on a piece of paper, cutting it out, and taping the two ends together to form acontinuous ring. As you made a complete traversal of the ring, you would encounter two peaks.)

However, the locations of the two peaks for the rightmost array are at completely different wavenumber values than are the peaks for the other twoarrays. The two peaks exhibited by the rightmost array are in the locations of the two nulls for the center array. Similarly, the null points for the rightmostarray are in the same locations as the two peaks for the center array.

What can we learn from these scenarios?

We learn that we can have a significant impact on the wavenumber response of an array by increasing the number of elements in the array. We can also have asignificant impact on the wavenumber response by applying weights, (including sign changes) , to the electrical signals produced by the array elements before adding them together.

Extending into two dimensions

Now let's complicate things a bit by extending our array analysis into two dimensions. Up to this point, we have assumed that our sensors were attached toa wire that was free to move up and down only. As such, waves impinging on the array were constrained to approach the array from one end or the other. In thiscase the wavenumber was completely determined by the wavelength of the wave.

(For our purposes, the wavelength is given by the ratio of propagation speed in meters per second to frequency in cycles per second.Canceling out the units leaves us with wavelength in meters per cycle.)

Move the array to a table top

Let's move our array of sensors from the wire to a large sheet of metal on the top of a table. For the time being, we will still place the elements in aline with uniform spacing. However, we will now assume that a wave can impinge on the array from any direction along the surface of the sheet of metal.

(For simplicity, we will assume that there is some sort of insulation between the sheet of metal and the table top to prevent waves from impinging on the array from below.)

What does a wave look like in this scenario?

Imagine a piece of corrugated sheet metal or fiber glass. (Material like this is sometimes used to build a roof on a patio.) When you look at it from one end, it looks something like the sine wave in Figure 1 . However, if you keep it at eye level and slowly turn it in the horizontal plane, the distance between the peaks willappear to become shorter and shorter until finally you don't see any peaks at all. What you see at that point is something that appears to have the samethickness from one end to the other. This is the view that one of our sensors sees as the wavefront of an impinging wave.

Questions & Answers

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
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
im not good at math so would this help me
Rachael Reply
yes
Asali
I'm not good at math so would you help me
Samantha
what is the problem that i will help you to self with?
Asali
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
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
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, 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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