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Uncertainty propagation

  1. Feb 5, 2008 #1
    1. The problem statement, all variables and given/known data

    Calculate "f" and its uncertainty, watch the units, show all work.

    2. Relevant equations

    f(x,z)= z/x
    x=100.5(+ or -) 3.8 cm
    y=71(+ or -) 1 s

    3. The attempt at a solution

    ok so i know that to find uncertainty i have to use the equation delta f(x,y)=df(x,y)/dx *(delta x) + df(x,y)/dy * delta y. I got (delta f)= z*lnx*(delta x) + (delta z)/x. When i plug in the numbers the units dont match up, i get cm*s + s/cm.

    im really confused on how to find the answer can someone please help. thanks.
     
  2. jcsd
  3. Feb 5, 2008 #2

    Hootenanny

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    That is not correct. In general:

    [tex]\left(\Delta f(x,y)\right)^2 = \left(\frac{\partial f}{\partial x}\right)^2\Delta x^2 + \left(\frac{\partial f}{\partial y}\right)^2\Delta y^2[/tex]

    This is also in correct.

    [tex]\frac{d}{dx}\left(\frac{1}{x}\right) \neq \ln|x|[/tex]
     
    Last edited: Feb 5, 2008
  4. Feb 5, 2008 #3
    oh jeez you're right thanks
     
  5. Feb 5, 2008 #4

    Hootenanny

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    Take a note of my further comment, which was added after you replied.
     
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