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Sound and wave interference

  1. Feb 15, 2017 #1
    1. The problem statement, all variables and given/known data
    Two trains approach the train station from opposite sides each moving at an initialvelocity of 120 km/h with respect to the station and slowing down to a halt in 20seconds. If both trains are whistling at 5000 Hz, find the distance between the zeroand first order maxima as a function of time.
    4-e89aee99f1.jpg

    so this is the question:
    when they say zero and first order maxima they mean it only lies on the x axis right meaning the zero order maxima is at the centre of the two trains and the first order maxima is at distance d away where the extra length travelled is exactly a wavelength so i did the question just for the part when the trains are not decelerating ie t=0 and my solution does not match the given one please help or is the first order maxima in the y direction
    2. Relevant equations
    f = fo [c/c-v] --- doppler effect for train approaching
    c= 331m/s
    λ = c/f
    v = 120/3.6 m/s
    the given solution is at t =0 the distance between the zero and first order is 893/60000 m

    3. The attempt at a solution
    the first order is offset to one side by distance d so
    2d is the extra length travelled the sound wave coming from the other side hence
    2d=λ
    2d = c/f
    2d = c(c-v)/(2c fo)
    plugging in gets me 893/30000 which is twice of correct answer please help
     
    Last edited: Feb 15, 2017
  2. jcsd
  3. Feb 15, 2017 #2

    BvU

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    True, but doesn't the one from the opposite side travel over a little less distance ?
     
  4. Feb 15, 2017 #3
    i am sorry i dont get what you mean could please explain your point thanks
     
  5. Feb 15, 2017 #4

    BvU

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    Make a drawing and you'll see it more easily. Constructive interference occurs where one wave travels ##{1\over 2}\lambda ## further and the other ##{1\over 2}\lambda ## less.
     
  6. Feb 15, 2017 #5
    oh i see it now thanks so much !!!!
     
  7. Feb 15, 2017 #6

    BvU

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    You're welcome :smile:
     
  8. Feb 15, 2017 #7
    no wait sir i did what you said and all of a sudden i am confused again as i once again get d =λ/2 please enlighten me as if one wave were to travel 1/2λ lesser it implies that that is d
     
  9. Feb 15, 2017 #8

    BvU

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    I made the drawing and find I have to correct myself: not ##{1\over 2}\lambda## but ##{1\over 4}\lambda## ... o:)

    Can you see why ?

    (It's astounding to see how much more instructive an animated picture is wrt one on paper ! How wonderful all these newfangled technologies o0) )
     
  10. Feb 16, 2017 #9
    thank you sir i figured out my mistake i was all along using cos graph for both side only to realise that when the two cos graphs collide they will super pose to zero at every point i should have used cos graph on one side and -cos graph on the other side and then your 1/4λ thing works thanks for your troubles really appreciate it !!!
     
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