Homework Help: Tricky error calculation

1. Jan 22, 2005

JamesJames

How do I calculate the uncertainty of

q = [exp(x/2)][t^(1/2)]

where both x and t have known uncertainties.

I could have done the thing if there was no exp(x/2) term. But that term is causing me a lot of stress.

I am really confused.
James

2. Jan 22, 2005

cepheid

Staff Emeritus
In one of my lab courses, we were given a short write-up on error analysis. It gave the formula that I'm going to put below. So you are trying to calculate a quantity q that depends on two other quantities you have measured (and therefore whose experimental uncertainties you know): x and t. Well, the uncertainty in both x and in t will affect the error in q, because q depends on both. Assuming that x and t are independent variables, the formula we were given for "Errors propagating through a functional relationship:"

$$\delta q^2 = \left(\frac{\partial q}{\partial t}\right)^2 \delta t^2 + \left(\frac{\partial q}{\partial x}\right)^2 \delta x^2$$

where delta q represents the uncertainty in q, for example. This formula makes sense to me sort of, because the uncertainty in q depends on the individual uncertainties in x and t, as well as the rate at which q changes with each one. For instance, if dq/dt (<--meant to be partial) is large, the even a small delta t will affect q significantly. However, a friend of mine with a math BSc was telling me that these formulas aren't strictly correct, and that you're not actually supposed to be doing calculus per se. Error analysis seems to me to be a very complicated, convoluted subject. Hopefully somebody here will be able to comment on whether using this formula is indeed the best method.

3. Jan 23, 2005

Dr Transport

At this time the formula that cephid quoted is correct. You have KNOWN errors, the problem arises when you do not know the errors. I have been reading alot about error calculation lately because my employer needs to know the no (&()&) error for some of the apparatuses we use and bought commercially. The calculation of errors is essentially a mathematical problem, a very complex mathematical problem. If you go to the NIST website (www.nist.gov[/url]) or the NPL ([url]www.npl.co.uk[/URL]) and look for uncertainty analysis you'll find a massive amount of material out there. A good place to start is with John Mandel, Statistical Analysis of Experimental Data, I have learned enough to be somewhat dangerous.

Last edited by a moderator: Apr 21, 2017