# Wave interference pattern

## Homework Statement

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

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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BvU
Homework Helper
2019 Award
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 ?

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.

The similar threads mentioned at the bottom aren't very useful. Perhaps this one is.
I can't find that in your problem formulation ?

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...

BvU
Homework Helper
2019 Award
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.

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.