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Waes: normal mode frequencies for 1 fixed extremity

  1. Mar 27, 2008 #1
    1. The problem statement, all variables and given/known data

    A String of length L has one of its extremities fixed and the other one loose.

    A. What's the equation for the normal mode frequencies?
    B. Draw a snapshot of the string for the 1st 3 normal modes

    2. Relevant equations
    wave equation

    3. The attempt at a solution

    My idea was to follow the same line of thinking for a string with both extremities fixed. Then we can assume that

    y(x, t) = g(x).cos(wt + d) --(1)

    and (1) must be solution of the wave equation, and after some math we get the general solution

    A(x)'' + A.k^2 = 0, k = w/v --(2)

    we know that A(0) = 0, since the x=0 extremity is fixed and the general solution for 2 is

    A(x) = b.cos(kx) + c.sin(kx)

    so, b = 0 and A(x) = c.sin(kx)

    since A(x) != 0, we know that c != 0, but there's no other known condition in order to compute possible values for k

    any ideas? and.. tbh i dunno if i can assume everything i did since 1 of the extremities is loose. help pls! :D
  2. jcsd
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