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Radio Wave Interference

  1. Feb 19, 2006 #1

    G01

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    Two radio towers are positioned 10m apart. They emit waves of 750mHz. How many maxima will you detect if you walk around the towers in a circle of radius=10m?

    I know that the path length difference, [tex]\Delta r [/tex], must = an integer number of wavelengths:

    [tex] \Delta r = n\lambda [/tex]

    Where I'm confused is how to find an expression using this information to solve for the number of maximas in a circle. Can anyone give me any hints? I'd show more work if I could think of anything else. The only other work I have is solving for the wavelength:

    [tex] c = \lambda f [/tex]

    [tex] \lambda = \frac{c}{f} = \frac{3X10^8m/s}{750000000Hz} = .4m [/tex]
     
  2. jcsd
  3. Feb 19, 2006 #2
    It looks like 2, since
    [tex]d \sin(\theta) = \pm \lambda[/tex]
    [tex]\sin(\theta) = \pm 1[/tex]
    with in [tex]0, 2\pi[/tex] interval
    [tex]\theta = \pi, 3 \pi /2[/tex]
     
  4. Feb 19, 2006 #3

    G01

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    The answe is 20, which is what is confusing me. I got 2 also, but at [tex] \pi/2 , 3\pi/2 [/tex] I don't know how I'm supposed to find the 20 spots. I know there has to be a way to derive a formula for it. Or something.
     
  5. Feb 20, 2006 #4
    What the heck I've done, the wavelength isn't 10m, it's 0.4m! Plus, 0 is also an integer, so there would be 4 solution (yours and mine should add, if d=wavelength!) Oh my! I was totally sleepy!

    So then, let me try again. The difference in distance of waveves should be [tex]10 \sin(\theta)[/tex], and if this difference is equal to 0 or an integer multiple of wavelength, then there should be a maxima
    [tex]25 \lambda \sin(\theta) = n \lambda[/tex]
    [tex]\sin(\theta) = [-1,1] = n/25[/tex] where n is an integer.

    Hmm.. I still don't have 20. I don't know where I got wrong, though.
    I assumed center of the circle is in the middle of towers, BTW.
     
  6. Feb 20, 2006 #5

    G01

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    Sorry I screwed up. The distance between the towers is 2 m not 10.
     
  7. Feb 20, 2006 #6

    G01

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    Ok, I found that the angles, 0, [tex] \pi/2, \pi, 3\pi/2, [/tex] all have maximas so that gives me four. Now i need to find a way to find the maximas in one of the quadrants and I can multpily that by four and then add four to that and I should get 20. Im lost on how to find the maximas in between quadrant angles. How do you get the the distance between waves is [tex] 10\sin(\theta) [/tex]
     
  8. Feb 20, 2006 #7
  9. Feb 20, 2006 #8

    G01

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    im sorry, i don't know which sectionyou want me to look at. I read the page and I have seen most of that stuff, but I don't see what section answers my question about why the distance bewteen the waves equals 10sin(x),
     
  10. Feb 20, 2006 #9
    "Constructive Inteference" section
     
  11. Feb 20, 2006 #10

    G01

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    i got the answer thanks.
     
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