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Circular Wave Fronts Emitted by Two Wave Sources

  1. Jun 18, 2016 #1
    1. The problem statement, all variables and given/known data
    https://session.masteringphysics.com/problemAsset/1383558/3/21.EX26.jpg

    Make a table with rows labeled P, Q, and R and columns labeled r1, r2, Δr, and C/D. Fill in the table for points P, Q, and R, giving the distances as multiples of λ and indicating, with a C or a D, whether the interference at that point is constructive or destructive.



    3. The attempt at a solution

    Okay, so I am not entirely sure I am doing this right. I have two attempts and used one. Can someone help me with this?

    Here's my new answer


    R1 R2 Δr C/D
    P 2λ 3λ λ C
    Q 3λ 2λ λ D
    R 2.5 3λ 0.5λ C

    Would you say this is correct?

    Sorry, the graph is out of place. idk how to forumat
     
  2. jcsd
  3. Jun 18, 2016 #2
    Surely the distances can only be integer multiples of λ if they lie on the circles?
     
  4. Jun 18, 2016 #3
    I'm not quite sure what you are getting at here. Care to elaborate?
     
  5. Jun 18, 2016 #4
    Well, it looks like the circles are evenly spaced so presumably they are spaced at a distance of one wavelength from each other.
     
  6. Jun 18, 2016 #5

    Oh yes I now understand. Yeah, they are spaced evenly. My problem is more along the lines of whether I counted right or not. I just wanted an outside confirmation
     
  7. Jun 18, 2016 #6
    There are a couple of errors, for example, R2 for P which is why I was making the point about integer multiples lying on the circles. You should also take another look at the C/D column.
     
  8. Jun 18, 2016 #7
    So should R2 be 3.5? Because that was what I initially thought but my answer choices lack a 3.5

    Also, I'm not sure about anything regarding the C/D column
     
  9. Jun 18, 2016 #8
    Ah, looking at the diagram again, I think 3 might actually be correct. If you look at the first circle around 2 it seems to be around half the radius of 1 so I'd assume that the circles about 2 are 0.5λ, 1.5λ, 2.5λ... So you should probably take another look at R2 for Q.
     
  10. Jun 18, 2016 #9

    So R2 for Q would be 1 as opposed to 2?
     
  11. Jun 18, 2016 #10
    The first circle appears to be 0.5λ away from 2, each other one appears to be spaced 1λ apart.
     
  12. Jun 18, 2016 #11

    So 1.5?
     
  13. Jun 18, 2016 #12
    I think that'd be correct. As for the C/D column, if these circles are one wavelength apart then the circles must represent unique points on the wave over one wavelength. If you consider a sine/cosine curve over one wavelength you can see that all values of y appear for 2 values of x with the exception of the peak and the trough, therefore the circles must represent either a peak or a trough. If you imagine the peaks to be at the circles then the troughs should be mid way between the circles.
     
  14. Jun 19, 2016 #13
    Okay I've updated. Mind telling me if this is sound?

    R1 R2. Chng. R c/d
    P. 2. 3. 1. C
    Q. 3. 1.5. 1.5. D
    R. 2.5. 3. 0.5. D
     
  15. Jun 24, 2016 #14
    Sorry, didn't see that you'd responded. You've probably submitted your solution by now, but just incase you're still on it, I think that everything is correct except for the C/D column. If the circles represent peaks then, for example, with P it's on a peak for 1 and a trough for 2 causing destructive interference.
     
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