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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?

    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


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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


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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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