1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

  1. Feb 7, 2010 #1

    morrobay

    User Avatar
    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

    User Avatar
    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

    User Avatar
    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

    User Avatar
    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
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Y displacements in sine wave at (x) and (x + 2 wavelengths)
  1. |x-y|+|x|-|y| <= 2 (Replies: 1)

  2. Y`= (x^2 + y^2)/xy ODE (Replies: 7)

Loading...