Determining Wave Parameters for Interference Pattern

In summary: If the wavelength is 7 mm and the slits are 23 mm apart, I expect more than four node lines to point to the zone between the slits.
  • #1
ilii
39
1

Homework Statement


Using the two-dimensional wave interference pattern shown and the two equations involving path difference, complete the following:

(please see attachment)a)Measure the wavelength of the waves, the distance between the sources, and the path distance from each of the sources to point P.

b)Choose a point on any antinodal line and show the complete calculation for wavelength.

c)What effect would an increase in frequency have in the interference pattern?

d)What effect would decreasing the distance between the wave sources have on the interference pattern?

e)If the phase of the vibrating sources were changed so they were vibrating completely out of phase, what effect would this have on the interference pattern?

Homework Equations


|PnS1-PnS2|=(n-1/2)W
|PmS1-PmS2|=mW

where W=wavelength

The Attempt at a Solution


all approximated (measured with a ruler)

W= 7mm
dS1S2=23mm
PnS1=62mm
PnS2=81mm

|PnS1-PnS2|=(n-1/2)W
|62-81|=(1-1/2)W
-19=(1/2)W
W=-38 ?

All I need is a bit of direction here on part a and b. The textbook is confusing with the examples it provides and I find this question confusing as well. After I measured the wavelength, it wants me to find the wavelength using the measured wavelength? What am I trying to find? My answer is obviously way off and substituting n=2 only gives me -12.6 for W. After I measure the wavelength, what then?

any help on this question is appreciated, thank you

 

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  • #2
The similar threads mentioned at the bottom aren't very useful. Perhaps this one is.
After I measured the wavelength, it wants me to find the wavelength using the measured wavelength?
I can't find that in your problem formulation ?

I can't follow your equations: what are the other variables ?

W = wavelength is difficult to get used to. Most folks use ##\lambda## (type ##\#\### \lambda ##\#\### ) or λ from the list you get when clicking the ##\Sigma## on the toolbar.
 
  • #3
BvU said:
The similar threads mentioned at the bottom aren't very useful. Perhaps this one is.
I can't find that in your problem formulation ?

I can't follow your equations: what are the other variables ?

W = wavelength is difficult to get used to. Most folks use ##\lambda## (type ##\#\### \lambda ##\#\### ) or λ from the list you get when clicking the ##\Sigma## on the toolbar.
λ= 7mm
dS1S2=23mm (distance between the two sources)
PnS1=62mm (source 1 to the node point)
PnS2=81mm (source 2 to the node point)

I was only given these two equations:
|PnS1-PnS2|=(n-1/2)λ
|PmS1-PmS2|=mλ


where m=the antinode

Maybe I just need help understanding what the question is asking. I am not sure what is meant by "Measure the wavelength of the waves, the distance between the sources, and the path distance from each of the sources to point P." and then it asks me to "Choose a point on any antinodal line and show the complete calculation for wavelength.". If it asks me to 'measure the wavelength of the waves" ... then asks me to "show the complete calculation for wavelength"... how are these two dissimilar and how would I go about finding the complete calculation for wavelength? I thought I measured the wavelength already. I must be missing something fundamental...
 
  • #4
You attached a picture to post #1 from which nothing at all can be measured. So it's difficult to comment on what you measured. Is this really where you had to make your measurements? I see an S1 and an S2 . No point P. No Pn and no Pm either.

Did you check the pictures in the link I mentioned ?

If the wavelength is 7 mm and the slits are 23 mm apart, I expect more than four node lines to point to the zone between the slits.

There is one antinode line where m = 0, so you know what n is on each of the node lines in the picture.

ilii said:
I am not sure what is meant by "Measure
1) the wavelength of the waves,
2) the distance between the sources, and
3) the path distance from each of the sources to point P."
Well, it can't be 2) or 3), can it ? You'll need to explain the cause of this uncertainty for a potential helper.
 

FAQ: Determining Wave Parameters for Interference Pattern

What is a wave interference pattern?

A wave interference pattern is a phenomenon that occurs when two or more waves interact with each other. It is characterized by the overlapping and superposition of the individual waves, resulting in areas of constructive and destructive interference.

What causes a wave interference pattern?

The interference pattern is caused by the interaction of two or more waves with similar frequencies and wavelengths. When these waves meet, they combine and either reinforce or cancel each other out, creating the interference pattern.

What are the types of wave interference patterns?

There are two types of wave interference patterns: constructive interference and destructive interference. Constructive interference occurs when the waves combine to create a larger amplitude, while destructive interference occurs when the waves cancel each other out and create a smaller amplitude.

What is the significance of wave interference patterns?

Wave interference patterns have significant applications in various fields such as optics, acoustics, and electronics. They are used to study the properties of waves and can help in understanding the behavior of complex systems.

How can wave interference patterns be controlled or manipulated?

Wave interference patterns can be controlled or manipulated by changing the amplitude, frequency, or phase of the waves. This can be achieved through the use of devices such as mirrors, lenses, and diffraction gratings.

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