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Wave equation diagram problem

  1. Jan 7, 2015 #1
    1. The problem statement, all variables and given/known data
    The question is to sketch for values of t = 0, t =0.25, t = 0.5, t=1 and t = 1.25 for the wave equation

    Ytt = Yxx in the infinite domain with initial conditions

    y(x,0) = f(x) =
    \begin{cases}
    1 & \text{if } 0 ≤ x ≤ 1 \\
    & 0 (otherwise)
    \end{cases}

    Yt(x,0) = 0



    2. Relevant equations
    Y(x,t) = a(x,t) + b(x,t)

    where a(x,t) = ## \frac {1} {2} \ ## f(x+t)
    and b(x,t) = ## \frac {1} {2} \ ## f(x-t)

    3. The attempt at a solution
    These are the sketches I obtained for those times and they are not to exactly measured to the points as I did them in paint. Can someone please tell me if the sketches are correct for this question!

    upload_2015-1-7_12-21-36.png
    upload_2015-1-7_12-21-54.png

    for t =0

    upload_2015-1-7_12-22-40.png
    upload_2015-1-7_12-22-59.png

    for t= 0.25

    Attaching the remaining ones in the post below as you can't attach more than 6 in one post.
     

    Attached Files:

  2. jcsd
  3. Jan 7, 2015 #2
    upload_2015-1-7_12-25-50.png
    upload_2015-1-7_12-26-14.png

    for t = 0.5 s

    upload_2015-1-7_12-26-57.png
    upload_2015-1-7_12-27-18.png

    for t = 1 s
     
  4. Jan 7, 2015 #3

    BvU

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    Homework Helper
    Gold Member

    Hi JI,

    As you may know, PF has great difficulty handing out approval stamps: it could create big problems with teachers, exam committees and what have you. PF homework is meant to help folks when they get stuck; with hints, questions and advice. My personal opinion is you don't need any of those :)

    and ;)
     
  5. Jan 7, 2015 #4
    Look man can you be more clear? I don't understand what are you talking about. All I asked is if my sketches are correct or not, I am not asking you to do my homework for me.
     
  6. Jan 7, 2015 #5

    BvU

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    Gold Member

    Yes I can be more clear: I think what you did is excellent -- but you can't derive any rights from my statements.

    My post #3 tries to express some reluctance about the "Is this correct" questions.
     
  7. Jan 7, 2015 #6
    Cheers mate! I just realized I missed out t= 1.25 s for this question

    Can you see the sketches for t = 1.25 s are excellent as well

    upload_2015-1-7_16-56-53.png
    upload_2015-1-7_16-57-14.png
     
  8. Jan 7, 2015 #7

    BvU

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    Gold Member

    As I said: you're so good you don't need assistance here :)

    You do have me wondering what's the reason you ask for confirmation: you clearly understand everything that's going on, so why this possible doubt ?
     
  9. Jan 7, 2015 #8
    Cheers! I just want to be 100% sure that my works are correct so that I get full marks....so even if I understand everything I want to confirm with people who has more knowledge than me.
     
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