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Homework Help: Y displacements in sine wave at (x) and (x + 2 wavelengths)

  1. Feb 7, 2010 #1

    morrobay

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    Gold Member

    1. The problem statement, all variables and given/known data
    A sine wave in + x direction with max amplitude of 1
    wavelength= 2.85 m
    wavenumber, k = 6.28/2.85 m = 2.2 rad/m
    w=8rad/m
    frequency=1.27 cyc/sec
    vel.= 3.63 m/sec
    at x = 20m t= 5.5 sec
    at x + 2 wavelengths x= 25.7m t=7.07 sec
    by definition the y displacement is the same at (x) as it is at (x + 2 wavelengths)


    2. Relevant equations
    y (x,t)= A sin(kx-wt)


    3. The attempt at a solution
    just considering y= Asin(kx) at x= 20m ,y= .0177
    with y= Asin(k x+2 wavelengths) x= 25.7m, y=-.00866
    with radian set calculator
    I dont understand wht the y displacements are not the same

    Also if the other variables are put into the solution A=Aosin(kx-wt)
    then in both cases (kx-wt) =0 ?











    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
    Last edited: Feb 8, 2010
  2. jcsd
  3. Feb 9, 2010 #2

    rl.bhat

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    Homework Helper

    equation of a moving in +x direction can be written as
    y(x,t)= yo*sin2π(t/T - x/λ)
    Here x = 20 m. It can be written as n*λ + x'. Similarly t can be written as n*T + t'
    So 20 = 7*2.85 + x'. Or x' = 0.05 m.
    T = 2π/8 = 0.785 s.
    t' = T/λ*x' =.........?
    Rewrite the equation as
    y(x,t)= yo*sin2π(t'/T - x'/λ) and solve for y.
     
  4. Feb 10, 2010 #3

    morrobay

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    Gold Member

    thanks i cleared up my confusion with the correct values; with y=yo(sin2pi) x/wl -t/T
    at t=0
    x=20m
    wavelengh =2.85m
    T=.785s
    y=yo(sin2pi) x/wavelength y= sin44.07= .087
    then after wave travels two wavelengths
    x=25.7 m
    t=2T = 1.57s

    y=yo (sin2pi) 25.7m/2.85m - 1.57s/.785s =sin44.07=.087 checks out with above

    actually in your reply above i dont see how x' = .05m since two wavelenths is 5.7m
     
    Last edited: Feb 10, 2010
  5. Feb 10, 2010 #4

    rl.bhat

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    Homework Helper

    As I have indicated, the equation of wave moving in the positive x direction is
    y = yo*sin[2π(t/T - x/λ)]
    I presume, in the problem x , velocity. frequency, wavelength and yo is given.
    So the dispalcement y at x = 20 m can be found by
    y = sin[2π(5.5/0.785 - 20/2.85)]
    Now find y.
     
    Last edited: Feb 10, 2010
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