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Path difference between the waves

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  1. Nov 2, 2015 #1
    1. The problem statement, all variables and given/known data
    upload_2015-11-2_20-59-1.png

    2. Relevant equations


    3. The attempt at a solution
    I formed a right angle triangle between the arrow downwards,d, and perpendicular line x from arrow. As such, sin θ = x/d.

    x= d sinθ
    path difference: d sinθ/λ

    My answer is C, but answer is B. Where did cos θ come from?
     
  2. jcsd
  3. Nov 2, 2015 #2

    DrClaude

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    Staff: Mentor

    Looking at the figure, in which case would you expect it to be no difference in path length?
     
  4. Nov 2, 2015 #3

    gneill

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    Staff: Mentor

    Your description of how you formed your triangle is not very rigorous, so I may be misinterpreting what you've described. That said, I think you've allocated angle ##\theta## to the wrong corner of your triangle.

    Perhaps you could sketch your construction on the image and post the result?
     
  5. Nov 2, 2015 #4
    Is it when the waves are received at angle perpendicular to the horizontal?
     
  6. Nov 2, 2015 #5

    DrClaude

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    Which corresponds to which value of θ?
     
  7. Nov 2, 2015 #6
    90°?
     
  8. Nov 2, 2015 #7
    upload_2015-11-2_21-26-47.png
    I did it this way, but I think now I'm wrong to assume that x is parallel to the wavelength, right?
     
  9. Nov 2, 2015 #8

    gneill

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    You've drawn the correct triangle but as you say, you've chosen the wrong "leg" for x. You want the leg that lies along the wave's path.
    Fig1.png
     
  10. Nov 2, 2015 #9
    Ah, I see now why it's cos θ. But, why it is not D now? Shouldn't path difference be expressed in terms of fraction of wavelengths?
     
  11. Nov 2, 2015 #10

    gneill

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    In this case the path difference is just the length, otherwise the problem would have specified to express it in terms of wavelengths.
     
  12. Nov 2, 2015 #11
    Ok. Thanks!
     
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