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Snapshot and history graphs for a string under tension (drive mechanism)

  1. Mar 14, 2012 #1
    1. The problem statement, all variables and given/known data
    A string with mass density u = 9.00 g/m extends from zero to infinity along the x-axis. It is
    under tension T = 25 N, and is driven by a mechanism at x = 0.

    The velocity of the drive mechanism depends on time as:
    vy(t) =
    0 (if t = 0)
    10.0 cm/s (if 0 < t ≤ 0.1 s)
    −20.0 cm/s (if 0.1 s < t ≤ 0.2 s)
    10.0 cm/s (if 0.2 s < t ≤ 0.3 s)
    0 if t > 0.3 s

    (a) Sketch a “snapshot graph” of the displacement of the string at time t = 0.5 s, from 0
    to 30 m along the x-axis. Use a range of -1.0 cm to +1.0 cm on the y-axis.

    (b) Sketch the “history graph” at x = 10 m, for t = 0 to 0.6 s.

    2. Relevant equations
    v = sqrt(T/u)
    Y = Yo cos(kx - w t)

    3. The attempt at a solution
    I can calculate the wave speed from square root of (T/u)

    a) t = 0.5 s
    Therefore, vy(t) = -20.0 cm/s
    At x = 0,
    yo = -20.0 * 0.5 = -10.0 cm
    But I do not know how y will vary with x. I thought of using
    Y = yo cos(k x), where k is wave-number.
    But do not know how to calculate the value of k as I do not know how to find wavelength or frequency.

    b) x = 10 m
    How do I find vy(t) at this value of x ?
     
  2. jcsd
  3. Mar 14, 2012 #2
    I realised the graphs will not be sinusoidal. They will have straight lines. I have made history graph at x = 0
    I calculated v = 52.7 m/s

    How to draw snapshot graph at t = 0.5 s and history graph at x = 10 m ?
     
  4. Mar 14, 2012 #3
    Snapshot is to be drawn at t = 0.5
    vy(t) = 0 at t = 0.5

    So can we say that the snapshot graph at t = 0.5 will be a single straight line coinciding with x axis?
     
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