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How to Combine Gradient Uncertainty with other Uncertainty?

  1. Mar 31, 2016 #1
    1. The problem statement, all variables and given/known data
    I did an experiment to measure the speed of sound(using two microphones and a hammer). I changed the distance between the two mics and calculated(using a fast timer) the time taken for the sound to reach from the start mic to the end mic. I made a graph(distance on x axis, time on y axis) on excel using my results and added a line of best fit. I need error bars and the uncertainty in the gradient. Also, I need to combine the uncertainty from the gradient with the random uncertainty, calibration and scale reading uncertainty(from meter stick). How can I do this?

    2. Relevant equations


    3. The attempt at a solution
    I know the formula for random uncertainty and the Pythagoras-like formula for combining uncertainties. I just don't know how to combine all of this with the gradient uncertainty.
     
    Last edited: Mar 31, 2016
  2. jcsd
  3. Mar 31, 2016 #2

    mfb

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    2016 Award

    Staff: Mentor

    In general: include uncorrelated uncertainties in the individual datapoints, make sure your fit takes those uncertainties into account (not sure if excel can do that). Correlated uncertainties need a different approach.
     
  4. Mar 31, 2016 #3
    @mfb Thanks for the reply I did a little experimenting and I combined the random uncertainty for each of my times with the digital reading uncertainty(using ∆w^2 = ∆x^2 + ∆y^2 + ∆z^2, x = random uncertainty, y = scale/digital reading uncertainty, z= calibration uncertainty ) and also did the same with my distances. I then plotted these in my excel graph as a custom error bar for each of my points. Is this the correct way to go? How would I go about finding the uncertainty of the gradient now, with the vertical and horizontal error bars in my graph too?
     
  5. Mar 31, 2016 #4

    mfb

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    2016 Award

    Staff: Mentor

    Excel has a function for the uncertainty of parameters of linear functions, I don't know if you can also directly get them from a trend line, and I don't know if the uncertainties are taking into account properly (change them to see if the result changes).
     
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