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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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?
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1answer
55 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 ...
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1answer
39 views
Error conversion [on hold]
$\alpha_L = \frac{1}{a}\frac{da}{dT}$
I know error in $a$, i.e., $da$
I need to find out $d\alpha$ from data of $da$.
$d\alpha_L = -\frac{1}{a^2}\frac{da}{dT}da$
Is this correct?
Note:
...
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3answers
103 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 ...
25
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6answers
5k 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 ...
5
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1answer
150 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?
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1answer
56 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 ...
8
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3answers
97 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 ...
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1answer
68 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 ...
4
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1answer
101 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 ...
5
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2answers
106 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 ...
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3answers
268 views
Basic vector addition problem [closed]
This is the entire problem:
A student adds two vectors with magnitudes of 200 and 40. Taking into account significant figures, which is the only possible choice for the magnitude of the resultant?
...
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1answer
63 views
How uncertainties affect values
If I calculate the equivalent resistance of a circuit, for example:
$$1/R_{eq} = 1/R_1 + 1/R_2 + 1/R_3 = 1/1472 + 1/3260 + 1/5580 \Rightarrow R_{eq} = 858.22\,\Omega$$
And then calculate its ...
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1answer
65 views
Measurement uncertainty basics
$$x = (\overline{x}-K)\pm \Delta x\tag{1}$$
$$\Delta x = s_{\overline{x}} = \sqrt{\frac t {\sqrt n} s_x} \tag{2}$$
$$s_x = \sqrt{\frac 1 {n-1} \sum^{n}_{i=1}(x_i-\overline{x})} \tag{3}$$
$$\frac ...
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1answer
109 views
Paper in physics - calculations; rounding or not?
I'm currently a high schooler, and I'm writing my first scientific paper. The result is fairly simple, and it is nothing too special, but I see it as a nice way to prepare myself for the academic ...
3
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1answer
65 views
Notations for statistical / systematic / numeric errors?
I constantly see the notation
$$
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 ...
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3answers
204 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{±\ ...
2
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1answer
66 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
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1answer
327 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
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1answer
123 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
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0answers
40 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 ...
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0answers
37 views
Error calculation from measures in a Stephan-Boltzmann experiment
If we are taking values from an experiment and we have them ordered in vectors as this:
Temperature: 55, 56, 67, 77, 56, 124, 56,
Voltage: 5. 23, 12, 12, 12, 12, 34, 34
$$ ...
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0answers
186 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 ...
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0answers
47 views
Uncertainty analysis of discrete derivative
Let's take evaporation case as a example. A water tank is mounted on a scale (resolution-$1g$) for evaporation. The scale auto record the result every $1s$. If the value changes at time $T$, ...
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1answer
60 views
Uncertainty in approximated relation
I'll give directly an example to fix the ideas. Suppose that you're studying the acceleration of a system of masses that depends from the number $n$ of masses $m$ by the following relation:
...
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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 ...
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0answers
44 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 ...
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1answer
68 views
How many measurements should be done? [closed]
I am measuring time of a computer operation. The operation should run roughly same time each time I measure it. How many times should I measure it to get good average and standard deviation?
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1answer
109 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
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1answer
179 views
Center of mass error - calculating systematic error in change in PE
Suppose we have to calculate systematic error in change in PE. Let's suppose systematic error due to scale is 1%. I'm confused about the center of mass error.
\begin{align}
\Delta PE = m*g*h_1 - ...
4
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2answers
735 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 ...
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3answers
150 views
Error calculation with linear regression
I am trying to determine the boltzmann constant by using a bipolar junction transistor.
In my circuit (apparently I don't have enough point to join a image sorry), the Ebers and Moll model gives the ...
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0answers
154 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
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1answer
124 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
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2answers
71 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 ...
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0answers
94 views
About the resolution/$\sqrt{12}$ uncertainty
Suppose you want to measure a (real-valued) quantity with an apparatus which will return as a result of the measurement the closest integer to the true value of the quantity.
Then, a common use is to ...
5
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2answers
219 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 ...
3
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2answers
1k 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 ...
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1answer
404 views
Two cylinders with same volume but different dimensions
If there are two cylinders (A and B) both with the same volume. B's radius is half of A's, so the length of B must be 4 ($2^2$) times that of A.
The uncertainty for the radius of A is the same as ...
2
votes
1answer
94 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
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1answer
80 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?
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1answer
69 views
How can I cheat an XRD sample (~10 mg) from a total 1g required? How can I use for the background.
How much can affect (in terms of hump) my X-ray diffraction pattern the "amorphous" glass or maybe someone can suggest me other material to compensate for the small amount of the sample.
Note: my ...
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1answer
53 views
Statistical error in a regression
I measured some voltage values ($x$) and some corresponding frequencies ($y$). I know that the voltage can only be measured within an uncertainty $\Delta x$. And the uncertainty of $y$ shall be ...
2
votes
2answers
488 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
0answers
836 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 ...
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1answer
84 views
Calculating uncertinity in measurements [closed]
I have a question relating to uncertinity.The equation used is period of a pendulum.
T=2π √(l/g)
For example consider time to complete 10 cycles by the pendulum as 19.6 (+/- 0.2)s.
I want to know ...
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2answers
1k 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 ...
2
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0answers
188 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 $p_i$. ...
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3answers
294 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?
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0answers
452 views
Error Analysis, Change in momentum, Kinetic Energy
If momentum of an object is increased by 10%,then its kinetic energy will be increased by?
Well, I don't need the solution logically by calculating the change in Kinetic Energy etc, but my question ...
