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Transverse waves

  1. Apr 20, 2009 #1
    The transverse displacement of an harmonic wave on a stretched rope is y = 0.04 cos(2.5 x - 5 t), where x and y are in meters and t is in seconds.

    a) What is the amplitude of this wave?
    A = m *
    .04 OK

    b) What is the wavelength of this wave?

    c) What is the speed with which this wave travels?

    d) In what direction is this wave propagating?
    +x

    e) What is the frequency (NOT the angular frequency) of this wave?
    f = s-1

    First off i need to find the wavelength. i am not sure where to start. in terms of the equation they gave me, idk how i can use that becuase it has 3 variables in stead of 2 so i cant plot it to figure out the wave length.. any ideas?
     
  2. jcsd
  3. Apr 20, 2009 #2

    Redbelly98

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    To get wavelength, fix t to be any constant ... use t=0 for convenience.

    You now have a periodic function in x, and the "period" of that function will be the wavelength.
     
  4. Apr 24, 2009 #3
    so my new equation would be:
    y=.04cos(2.5x) ? i get the wavelength to be 144 (just by graphing it) which is wrong
     
  5. Apr 24, 2009 #4

    Redbelly98

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    Yes, good.

    No. Try using radians, not degrees.
     
  6. Apr 24, 2009 #5
    ahh ok...2.51.

    now im kind of stuck as in velocity... no idea how to get it. equation is
    v=(wavelength* frequency)
    how do i determine frequency?
     
  7. Apr 24, 2009 #6
    These questions are most easily approached through the pure mathematical formula of waves

    The wave equation is
    D(x, t) = Acos(kx-wt) for a wave travelling in the positive x direction and d(x,t) = Acos (kx+wt) for a wave travelling in the negative x direction

    k is something called the wave number and is equal to 2Pi/wavelength, and w is called the angular frequency and is equal to 2pi*frequency. These are the mathematics of transverse waves.

    Look at your equation of the travelling wave, and you should be able to solve for everything you need :)
     
  8. Apr 26, 2009 #7
    ahhh ok..wow that made everything clear..thanks
     
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