Techniques and methods for computing, estimating, or placing bounds on the errors of expressions (formulas) based on knowledge of error distributions, error intervals or bounds of variables and parameters entering those expressions, and of methods used in the computations.

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5
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2answers
359 views

Why propagation of uncertainty is linear?

I'm in doubt with one thing: let's imagine that we have $n+1$ quantities, $n$ of them being directly measured, and the other one being related to the first $n$ by a function $f : \mathbb{R}^n \to ...
9
votes
3answers
6k views

How to combine measurement error with statistic error

We have to measure a period of an oscillation. We are to take the time it takes for 50 oscillations multiple times. I know that I will have a $\Delta t = 0.1 \, \mathrm s$ because of my reaction ...
3
votes
2answers
6k views

How to combine the error of two independent measurements of the same quantity?

I have measured $k_1$ and $k_2$ in two measurements and then I calculated $\Delta k_1$ and $\Delta k_2$. Now I want to calculate $k$ and $\Delta k$. $k$ is just the mean of $k_1$ and $k_2$. I thought ...
2
votes
2answers
2k views

When do I apply Significant figures in physics calculations?

I'm a little confused as to when to use significant figures for my physics class. For example, I'm asked to find the average speed of a race car that travels around a circular track with a radius of ...
38
votes
8answers
7k views

Why does the speed of light in vacuum have no uncertainty?

I could understand that the definition of a second wouldn't have an uncertainty when related to the transition of the Cs atom, so it doesn't have an error because it's an absolute reference and we ...
5
votes
5answers
506 views

The approximate uncertainty in $r$

The volume of a cylinder is given by the expression $V=\pi r^2 h$ The uncertainties for $V$ and $h$ are as shown below $\begin{align} V&\pm 7\%\\ h&\pm 3\% \end{align}$ What is the ...
-4
votes
3answers
442 views

Significant Figures [closed]

Subtract 0.2 J from 7.26 J. Express your answer to the correct number of significant figures for the given data. I think its 7, but the answer is 7.1. HOW?
6
votes
2answers
4k views

Multiple measurements of the same quantity - combining uncertainties

I have a number of measurements of the same quantity (in this case, the speed of sound in a material). Each of these measurements has their own uncertainty. $$ v_{1} \pm \Delta v_{1} $$ $$ v_{2} \pm ...
1
vote
2answers
110 views

Which error propagation equation to use for a function of 2 variables?

So I have been taught two formulas for error propagation: For $Z=A+B$, $\sigma_Z=\sqrt{(\sigma_A^2+\sigma_B^2)}$ and for Z=AB or Z=A/B ...
5
votes
2answers
138 views

Why is propagation of uncertainties quadratic rather than linear? [duplicate]

1) Up until now, during practical work sessions, I always used these formulas for uncertainty propagation: if $C = A+B$ or $C = A-B$ $$\Delta C = \Delta A + \Delta B$$ if $C = AB$ or $C = ...
1
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3answers
3k views

No uncertainty for standard gravitational acceleration?

The other day I asked about the uncertainty of light, and this issue triggered me to start looking into other physical constants and try to understand why other constants have no uncertainty. One of ...
4
votes
1answer
307 views

How do I calculate the experimental uncertainty in a function of two measured quantities

I am performing an experiment where I'm measuring two variables, say $x$ and $y$, but I'm actually interested in a third variable which I calculate from those two, $$z=f(x,y).$$ In my experiment, of ...
3
votes
2answers
280 views

Significant figures vs. absolute error

On NIST Avogadro's Number, $N_A = 6.022\;141\;29 \times 10^{23} \text{ mol}^{-1}$ has 9 significant figures and a standard uncertainty of $0.000\;000\;27 \times 10^{23} \text{ mol}^{-1}$. First, can ...
3
votes
1answer
204 views

Notations for statistical / systematic / numeric errors?

I constantly see the notation $$ 5.143(13) $$ for specifying that a value was measures / calculated to be 5.143 with an estimated error of 0.013. I have come to wonder though, just how commonly ...
3
votes
2answers
3k views

Calculating uncertainty in the final result (combining uncertainties)

I'm struggling to determine the uncertainty in $F$ so it would match the textbook answer. The problem statement is: A force F is obtained using the equation: $F = \frac{mv^2}{2\pi(x_2 - x_1)}$. The ...
2
votes
3answers
59 views

Why aren't calculation results in error propagation at the center of the range?

We have two copper rods, with $L_1$ and $L_2$ as their lengths respectively, and we want to glue the two bars together, with glue that's infinitesimally thin. $$\begin{align} L_1 &= 20 ± 0.2\ ...
1
vote
0answers
319 views

Combining errors to calcuate the total error (standard deviations)

I have a measurement method for which I want to study the measurement error by an error budget. Therefore, I listed all possible errors (error sources) (lets say $x_1, x_2, x_3,\ldots$). For each ...
3
votes
3answers
496 views

Accuracy and Error of Atomic Clocks

I'm quoting a passage from my notes: The development of clocks based on atomic oscillations allowed measures of timing with accuracy on the order of $1$ part in $10^{14}$, corresponding to errors ...
3
votes
1answer
777 views

Is $\sigma$ or $\sigma / \sqrt{N}$ is error of a measurement?

I wonder whether $\sigma$ or $\sigma / \sqrt{N}$ is error of a measurement. When I measure, say $0, 1, -1, 1, -1$, I have a $\sigma = 1$. I just measure $0, 1, -1$, I also have $\sigma = 1$. But in ...
2
votes
1answer
120 views

What are anticipated events and experimental uncertainty?

I am working on this lab that involved gathering data from two different sources. It involved gathering reaction times from a device and from a web application which was put into our data sets. It is ...
2
votes
3answers
6k views

Wheatstone Bridge

Why is using a Wheatstone bridge such an accurate way of calculating an unknown resistance? What are the benefits of using it over Ohm's law? It seems that it has something to do with the wires ...
1
vote
1answer
2k views

Relative error of equivalent resistance of resistors in parallel

I just saw a formula in my book for relative error in equivalent resistance of two resistors connected in parallel. $\frac{\Delta R}{R^2} = \frac{\Delta R_1}{R_1^2}+\frac{\Delta R_2}{R_2^2}$ ...
1
vote
1answer
3k views

Calculating the Uncertainty for an Average Value [closed]

How would I calculate the uncertainty for the average of this set? $32.5 \pm 0.1$ $32.0 \pm 0.1$ $32.3 \pm 0.1$
1
vote
1answer
119 views

Variance of Nested Experimental Uncertainty

I have to find the uncertainty of a quantity $Q$ doing two mean values. For example for a set of parameters I measure ten times $Q$, I obtain a mean value $Q_1$ and variance ${\rm Var}(Q_1)$. Then for ...