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Waves and light (problem solving)

  1. Oct 16, 2011 #1
    1. The problem statement, all variables and given/known data

    two speakers producing exactly the same frequency and always in phase are located on an east-west line emitting sound toward the north. the speakers are 30cm apart and a microphone is loacted 40cm due north of one speaker. which of the following wavelengths would produce sound with the intensity at the locations of the microphone?

    2. Relevant equations

    Xn/L = (n-1/2)λ/d

    or

    Δx/L = λ/d

    3. The attempt at a solution

    i know d=30cm
    L=40cm
    and n=2
    but i dont know where to get Xn (if that is the proper equation to use for this question)

    also the answer is 20cm
    please help me, i have no idea how to solve this question to get that answer.
    thank you
     
  2. jcsd
  3. Oct 16, 2011 #2

    Doc Al

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    Staff: Mentor

    Are you looking for constructive or destructive interference? (Most intensity or least intensity?) What wavelengths did they give?
     
  4. Oct 16, 2011 #3
    the question i posted above are the only information given to me:
    i beieve they are looking for the least intensity at the location of the microphone?
     
  5. Oct 16, 2011 #4

    Doc Al

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    Staff: Mentor

    OK, so do you want destructive or constructive interference? And what's the criteria for each?

    Hint: You must compare the path lengths from each speaker to the microphone.

    (When I read "which of the following..." I can only assume they gave you a list of choices.)
     
  6. Oct 16, 2011 #5
    oh yeah sorry, i forgot to add the options:
    a)5.0cm
    b)1.0cm
    c)20cm
    d)30cm
    e)40cm

    and the answer is 20cm
     
  7. Oct 16, 2011 #6

    Doc Al

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    Staff: Mentor

    Good. Now answer my questions:
    What's the difference in the path lengths from each speaker to the microphone? How does that path length difference relate to phase?
     
  8. Oct 16, 2011 #7
    so one speaker to the microphone is 40cm
    and to the other it is (40^2-30^2 = 700^(1/2) = 26.4cm?)
    then the path difference is 40cm - 26.4cm =13.5cm?
    is this right?
     
  9. Oct 16, 2011 #8

    Doc Al

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    Staff: Mentor

    Right.
    No. The distance from the other speaker to the microphone is the hypotenuse of a right triangle. (Draw yourself a diagram.)
     
  10. Oct 16, 2011 #9
    oh yeah sorry,
    so its 50cm for the other speaker
    so the difference in path is 50-40=10cm

    then 10cm = (n-1/2)wavelength
    and n = 1 therefore the answer becomes 20cm

    is this right? thank you so much
     
    Last edited: Oct 16, 2011
  11. Oct 16, 2011 #10

    Doc Al

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    Staff: Mentor

    Exactly right.

    To get destructive interference, that path length difference must be an odd multiple of λ/2.
     
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