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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30
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8answers
6k views

Why does the speed of light 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 ...
9
votes
10answers
271 views

Could one measure a stick to an arbitrary precision by having its length estimated by enough people?

I remember reading somewhere that the problem of exact time-keeping on ships could have been solved a lot earlier than it was if somebody would have had the idea of keeping time with a whole array of ...
9
votes
3answers
2k 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 ...
8
votes
3answers
107 views

Correct expression for experimental data

I am doing practices at the laboratory. I have some doubts about how to express correctly the errors; I read some pdfs in Google but I can't solve these questions: Sometimes, it's correct to write ...
7
votes
2answers
890 views

The error of the natural logarithm

Can anyone explain why the error for $\ln (x)$ (where for $x$ we have $x\pm\Delta x$) is simply said to be $\frac{\Delta x}{x}$? I would very much appreciate a somewhat rigorous rationalization of ...
5
votes
2answers
228 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 ...
5
votes
3answers
240 views

Calculating the uncertainty of $r$, when $1/r^2$ is used

I have tried to search through the forums and the Internet, however I haven't been able to find a source I was able to understand fully. I have a distance $r$, with an uncertainty of $\mathrm{±\ ...
5
votes
2answers
126 views

Does a large uncertainty in a given value justify a large uncertainty in the result?

I'm working on a pre-lab for my Physics 1 lab session, and I had a debate with the person I carpool with (who is taking the algebra-based Physics 1 lab). We seem to be unsure about uncertainties, and ...
5
votes
1answer
160 views

Age of the universe and age of stars

The age of the universe is 13.798±0.037 billion years, yet the age of HD 140283 is 14.46±0.8 billion years, how this can be the case?
5
votes
2answers
2k 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 ...
4
votes
5answers
419 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
2answers
1k views

Do you round off insignificant digits in the middle of a calculation?

I have a question... Do you round with significant digits during each subcalculation of a problem or only when the entire problem is complete? Example: multiply the following number: $$1.8 \times ...
4
votes
1answer
107 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 ...
4
votes
1answer
146 views

Propagation of uncertainty when integrating or differentiating

Lets say I have a polynomial $ax^4 +bx^3 +cx^2 +dx +e$ and the uncertainties on each coefficient. Now I need to calculate the tangent at some points as well as some areas under this curve. How would I ...
4
votes
2answers
2k views

Wheatstone bridge galvanometer error

We had to measure the resistance of $R_x$, we balanced the Wheatstone bridge and did calculations. My question is: we didn't include galvanometer error into calculations. Why is that? I read that it's ...
3
votes
3answers
448 views

Calculating uncertainties for a final result

Say you are dividing 2 times with uncertainties: $$\frac{t_1}{t_2} ~=~ \frac{0.551s \pm 0.002s}{ 0.712s \pm 0.002s}.$$ After doing the calculations you get: $$\frac{t_1}{t_2} ~=~ 0.774 \pm ...
3
votes
2answers
3k 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 ...
3
votes
2answers
187 views

Question about uncertainty

Are $3.43\pm 0.04$ $\frac{\mathrm{m}}{\mathrm{s}}$ and $3.48$ $\frac{\mathrm{m}}{\mathrm{s}}$ within expected range of values? The answer is yes, but I do not clearly see why this is so. I appreciate ...
3
votes
1answer
63 views

Combining uncertainties - multiple measurements

I am trying to understand how to combine uncertainties when they are dependent and independent from each other. Using this formula : $$\delta z = \sqrt {\Biggl(\dfrac{\partial f}{\partial x} \delta ...
3
votes
1answer
88 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
0answers
157 views

Production vs. Collection, and Contaminants vs. Depositions, what might be missing in cold fusion research

I though cold fusion and LENR were discredited, but just a few days ago I found out that NASA is claiming LENR is real. So I thought if they're detecting something, what could it be, and why wasn't it ...
2
votes
2answers
127 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 ...
2
votes
3answers
123 views

Physics Standard Deviation

I am a physics enthusiast and I have a question: Why is it meaningless to express the '$\pm$' (standard deviation) value as a percentage?
2
votes
2answers
817 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 ...
2
votes
5answers
70 views

Addition according to significant digits

I have been studying about significant digits and addition rules and I can't quite digest the rules of addition completely. It states that in the answer number of decimal places will be equal to the ...
2
votes
2answers
2k 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
1answer
521 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
3answers
3k 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 ...
2
votes
2answers
1k views

Definition of Significant Figures

In my textbooks, significant figures are defined as: “Significant figures by definition are the reliable digits in a number that are known with certainty.” “A significant figure is the one ...
2
votes
2answers
72 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 ...
2
votes
1answer
97 views

How to quote answer when error is smaller than significant figures of data?

We have these rules: Can't quote answer to more significant figures than original data. Error quoted to one significant figure unless first significant digit is a one. In which case quote error to 2 ...
2
votes
1answer
79 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
1answer
183 views

Experimental measurement of volumetric flow rate

The other day I with my team had to measure the volumetric flow rate through a pipe only using a 2000 mm$^3$ volumetric flask and a chronometer. The end of the pipe discharged to the atmosphere. As we ...
2
votes
2answers
94 views

Asymmetric uncertainties

Inspired by these two question on tex.SX Asymmetrical tolerancing Asymmetric uncertainties with siunitx package I'd like to ask for a nice explanation for these kind of uncertainties, like ...
2
votes
1answer
94 views

Multimeter has a resistance

If a multimeter has a resistance (1M ohm, say) when measuring voltages how do I take that into account in my error?
2
votes
1answer
563 views

Calculating Expected Systematic Error in a Pendulum Experiment

I am a little confused by part c of problem 4.28 of Taylor's Introduction to Error Analysis book. A student measures the acceleration due to gravity by using a steel ball suspended by a light string. ...
2
votes
1answer
155 views

Precision and accuracy calculations

Precision is usually understood as the number or significant figures in some experiment. Accuracy is the difference between the best measurement and the real value. How are precision and accuracy ...
2
votes
2answers
42 views

How to calculate error of parallax and sextant based navigation?

First of all, why wasn't the sextant ever used for land navigation? The horizon is easier to see at sea, but land based sextants could be used in conjunction with artificial horizons (as at sea when ...
2
votes
0answers
130 views

How can systematic errors be calculated?

Usually, it is said that systematic errors can not be handled in a well-defined way, unlike statistical errors. My question(s): A) How can systematical errors be calculated for any experimental ...
2
votes
0answers
55 views

error propagation and collision in ideal gas

When dealing with gas, a statistical approach is needed because For N particles, you have to solve 6N equations which cant be done analytically. To know our time step for numerical solving, you can ...
2
votes
1answer
105 views

Is this the correct way to I combine multiple interdependant pressure readings?

I want to measure the density in different layers of a suspension. To do this I want to place pressure sensors at different heights. Let's assume that the sensors are not by orders of magnitude more ...
2
votes
0answers
1k views

How to calculate uncertainties of a natural exponential function?

(I apologize if this should be posted in mathematics, however I chose to post it here as it's technically about physics) I conducted an experiment in which position of items were shifted on an ...
2
votes
0answers
211 views

How do I do error calculus right using gnuplot as an example?

Given is a set of measurements with their respective errors for example an energy spectrum. In gnuplot one is to fit a function $ f(x;\{p_i\})$ depending on a variable $x$ and on fit parameters $p_i$. ...
1
vote
2answers
387 views

Vectors, Component Addition, and Significant Figures

I have two vectors $\vec{A}$ and $\vec{B}$ and I need to find the x- and y-components of $\vec{C} = \vec{A} + \vec{B}$. Here's what I have so far: $$|\vec{A}| = 50.0 \mathrm{m}, \theta = ...
1
vote
1answer
66 views

Too small error on the calculus of wavelenght

I have this function: $$\lambda=d \sin(\arctan(\frac{x}{z}))$$ and I want to find its absolute error. $d$ is a constant ($10^{-6}$), $x =(0.716 \pm 0.001)$ m, and $z=(1.000 \pm 0.001) $ m. For the ...
1
vote
1answer
132 views

Paper in physics - calculations; rounding or not?

I'm currently a high schooler, and I'm writing my first scientific paper. The result is fairly simple, and it is nothing too special, but I see it as a nice way to prepare myself for the academic ...
1
vote
1answer
125 views

Measurement uncertainty of the quantity, that is function of two others quantities

I'm trying to compute uncertainty for the density of the ball. I measured its radius 6 times, so I was able to compute the stastistical uncertainty (we call it uncertainty type A, I don't know, if ...
1
vote
2answers
30 views

What's the difference between average absolute error and relative error?

I am quite confused by both these terms. I would like to know what's the exact difference between both these terms and which one is more accurate.
1
vote
1answer
33 views

Significant digits of time divided by 10

We're testing the period of a pendulum in physics class by measuring the time it takes to complete 10 periods then dividing that by 10. Our timing equipment measures to the nearest 100th of a second. ...
1
vote
1answer
30 views

Small question about accuracy and precision

Let's say I have a law like this, $$D=\frac{c}{r}$$ where $c$ is a constant, $r$ a distance in meter. my measures of $r$ are [$0.02m$, $0.01m$], then $<r>=0.015m$ and $\delta r = \pm 0.005m$. So ...