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Determine max speed of point on string

  1. Apr 22, 2008 #1
    1. The problem statement, all variables and given/known data
    A 2.5 m long string that has a mass of 0.10 kg is fixed at both ends and is under a tension 30 N. (c) Determine the maximum speed of a point on the middle of the string.


    2. Relevant equations
    2 sinusoidal waves having same amplitude, frequency and wavelength / superposition

    y(x, t) = 2Asin(kx)cos(wt)


    3. The attempt at a solution
    I have no idea as to what to do to approach this. The point on the string is moving in simple harmonic motion, which can be modeled by y(x) = Asin(wt) and v(x) = Awcos(wt)
    so maximum velocity would be Aw. Is this right? how would you find A? I'm probably approaching this wrong. Could someone give me a hint?

    For parts (a) we had to solve for the speed of the waves on string, which was
    v = (T/u)^(1/2) = (30/0.04)^(1/2) = 27.39 m/s
    for part (b) the question was "when the nth harmonic is excited, there is a node 0.50 m from one end. what is n?
    wavelength = 2L/n
    distance between nodes = wavelength / 2 = 0.5
    wavelength = 1 m
    1 = 2(2.5) / n
    n = 5, 5th harmonic

    I included parts (a) and (b) to show that I did think about this problem, I just got stuck with C. any help would be appreciated
     
  2. jcsd
  3. Apr 22, 2008 #2
    The equation you gave,
    y(x,t) = 2Asin(kx)cos(wt)
    is an equation of two independent variables.

    Every point on the string is given by only a single parameter, x.

    To find the velocity of any given point at any given time, with respect to what variable do you have to differentiate y(x,t) by?
     
  4. Apr 23, 2008 #3
    right, so i need to differentiate y(x,t) with respect to t by keeping x constant
    to get
    v = -2Asin(kx)sin(wt)w
    but then how do i get Amplitude?
     
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