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.

learn more… | top users | synonyms (1)

0
votes
2answers
24 views

Which 'error' to choose random or absolute?

WIn the experiment, to measure the distance I used a ruler (the least digit is 0.5 cm) For each idep. variable step I repeated the experiment 10 times, and then calculated the standard deviation ...
0
votes
0answers
20 views

Basics of experimental error 'bookkeeping'

In scientific experiment, I know that it is very important to know the exact level of error contained in a result, but I am not sure what the correct procedure is to 'keep book' of these errors. I ...
2
votes
1answer
36 views

Measurements and errors

I've measured several values of $V$ and $I$ in a simple circuit to determine de value of a resistance $R$: $$R=\frac{V}{I}$$ I have a list of points $(V,I)$ with their corresponging error (from the ...
7
votes
2answers
189 views

How does uncertainty/error propagate with differentiation?

I have a noisy temperature (T) vs. time (t) measurement and I want to calculate dT/dt. If I approximate $dT/dt = \Delta T/\Delta t$ then the noise in the derivative gets too high and the derivative ...
2
votes
3answers
58 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\ ...
2
votes
2answers
173 views

error propagation with an integral

My question here is about how to determine the error of an integral given individual uncertainties in two parameters defining the function being integrated. I used a curve fitting function to ...
0
votes
0answers
19 views

Reporting uncertainty values measured using analog instruments

If an Ammeter has a graduation of 1 mA and we assume that the best we can read is half this range, i.e. 0.5 mA. In this case, one can read something like 37.5 mA, or 12.0 mA. So the reported value ...
-1
votes
3answers
43 views

Significant figures

How to calculate significant figures of a number? I got confuse as the number 28600 has 3 significant figure instead of 5. Anyone can explain?
0
votes
0answers
43 views

how to handle errors in this high-school experiment?

I'd like to conduct some measurements with my pupils in the high-school I'm teaching in, but I ran into some conceptual problems. I'd like to measure the (approximately constant) speed $v$ of an ...
1
vote
0answers
24 views

Error propagation log2

I have a quick question to report some numbers on an experiment. I made measurements of fluorescence in a titration of a chemical. The titrations were 1:2 serial dilutions so I report each ...
4
votes
2answers
360 views

Physical experiments - False positives

How is it made sure that something has been discovered, and not just noise? Is one discovery of something that is predicted considered to be enough (Higgs-particle)? What are the probabilities of a ...
6
votes
5answers
834 views

Number of significant figures

I am looking for an intuitive answer that will explain me why there are only two significant figures in say the number 1500. Also definition from wikipedia: The significant figures of a number ...
2
votes
4answers
60 views

Is there a maximum accuracy for positions in the universe?

I was thinking how, since an object in our universe can move from one position to another, it must have passed through all the positions between those two positions. (I am thinking it moved it a ...
0
votes
0answers
27 views

How can we calculate the standard deviation of multiple values with different uncertainties each?

For example, if I have a set of readings, like: 13.4 +/- 0.5 14.5 +/- 0.7 12.8 +/- 0.6 13.9 +/- 0.4 14.8 +/- 0.5 How do I calculate the standard deviation of ...
1
vote
1answer
44 views

Not direct/inverse proportion implies systematic error

We were doing error-analysis and my physics teacher said: A relationship between physical constants is either direct proportion or inverse proportion. If these are not true then there is a systematic ...
1
vote
1answer
42 views

# significant figures in calculations?

I was taught to use the same number of significant figures in my answer as the piece of data with the lowest number of significant figures, so I was a bit confused when the solutions manual for this ...
0
votes
0answers
15 views

Propagation of incertitude - specific example [duplicate]

I am setting up an experiment, where I know the force and the incertitude (delta) of that force. However, I need to graph the logarithm of that force with the incertitude of the log. Can someone help ...
0
votes
0answers
41 views

Thermistor calibration - estimation of number of reference temperature points needed

A thermistor changes resistance with the temperature in a non-linear way and follows the exponential Arrhenius equation. Two reference points, ice slush water and boiling water, are used for ...
1
vote
0answers
43 views

Error in setting $m_{proton} = m_{neutron}$

Is the following reasoning correct, I'm doing mostly relativistic calculations so basically all masses come in squares. Suppose I have some expression that contains both the proton and the neutron ...
0
votes
0answers
41 views

Simple question relating to physics prac reports

I am writing a physics practical report relating to the elasticity of materials relating to their momentum in a collision. I have values for the elasticities that are all within 2% of each other but I ...
0
votes
0answers
16 views

How to understand the uncertainty of quoted value of cosmic black body radiation?

Geiner's Quantum Mechanics - An Introduction quotes a alue of cosmic black body radiation, "$2.65 \pm 0.09 K$". How to understand this uncertainty? I have undergraduate mathematics degree and are ...
1
vote
2answers
506 views

Error calculation in parallel resistances

This is the question: There are two resistors with resistance values $R_1=100\pm3$ ohm and $R_2=200\pm4$ ohm. Find the equivalent resistance of parallel combination. According to what I've ...
0
votes
1answer
50 views

Propagation of uncertainty - which formula? [duplicate]

Can someone explain to me when do I use this formula ...and when do I use this one?
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 = ...
0
votes
2answers
103 views

How to calculate the error in measurments of derived quantities knowing the error in basic quantities?

I wonder how to calculate error of a derived quantity $z$ knowing the error of all quantities that $z$ depends on say $x$ and $y$. For example: Suppose I want to calculate the speed of a body ...
1
vote
0answers
57 views

Propagation of Error on Radius of a Circle

I need to calculate the radius of a circle and its error from the chord length $L$ and height $h$ from the chord to the circumference of the circle. I know the formula for $R$ to be $R = ...
2
votes
2answers
92 views

Significant figure rules [duplicate]

In a simple physics experiment, we take the average a few readings to reduce the random errors. I apply significant figure rules to these. Say we round off at each step: (8.0+9.0+10.0)/3 = 27.0/3 ...
1
vote
3answers
154 views

Theoretical uncertainty of a circuit's total resistance when made entirely of resistors

My question in short(ish) is: Will the fractional uncertainty of a circuit made entirely of resistors with equal fractional uncertainties be the same as the fractional uncertainty of those resistors. ...
1
vote
1answer
134 views

Measuring depth or height from sea level

How is the depth or height relative to sea level measured? Well, if it's near the ocean, it can be easily measured manually, but what if it is 100 km away from the sea? What method is used?
3
votes
1answer
30 views

Scale Factor on Error

I was gathering some data from the particle data group website and for many results it gives a value, an uncertainty and then a scale factor for the uncertainty. For instance, at here, where it gives ...
1
vote
1answer
180 views

Significant Figures in Physics

A string has linear density $10.0 \cdot 10^{-3} \, \mbox{kg/m}$ and is kept under a tension of 100 N. A sinusoidal transverse wave, with a wavelength of 0.30 m, is traveling in the positive direction ...
0
votes
2answers
184 views

Uncertainty in parenthesis

In a physics text book I read the following: $$e/m=1.758820150(44) ×10^{11} \mathrm{C/kg} $$ In this expression, $(44)$ indicates the likely uncertainty in the last two digits, $50$. How ...
4
votes
5answers
523 views

Why do the errors in a formula depend on how it's written?

Let there be an equation, let's say $V=IR$. Now when we write its error formula we write it as $$\frac{\Delta V}{V} = \frac{\Delta I}{I} + \frac{\Delta R}{R}.$$ Now let us take example values. For ...
2
votes
1answer
239 views

Combination of errors question [closed]

A resistance R is in series with an inductance L. At angular frequency ω the magnitude of the complex impedance Z of this combination is given by |Z|^2 = R^2 + (ωL)^2 . Find |Z|, and the error in |Z|, ...
2
votes
1answer
159 views

How do we find the accuracy of atomic clocks?

We say that atomic clocks are the most accurate clocks ever made, they may lose or gain $x$ seconds in $y$ years. How do we find this uncertainty because we do not have an ideal clock to compare with ...
2
votes
2answers
86 views

Weighted mean from data [closed]

Suppose we have 3 experimental groups measuring "x", they measure $$x_1=\mu_1\pm \sigma_1$$ $$x_2=\mu_2\pm \sigma_2$$ $$x_3=\mu_3\pm \sigma_3$$ In the 3 experiments, we have done N measurements of ...
0
votes
0answers
59 views

Propagation of uncertainty - proof that it is minimal

I am not really sure if this is the right SE community for this question, but, I swear, I haven't found any better. The problem is as follows: we have n distance sensors placed around a quickly ...
2
votes
1answer
491 views

What is the error in a ruler?

I'm having trouble understanding simple error analysis of a ruler. Suppose we have this ruler. There is a mark for every centimeter. The precision is half a centimeter. This should mean that the ...
3
votes
1answer
172 views

error propagation with different plus and min errors and data fitting

I am refreshing my memory on error propagation and data fitting (Levenberg-Marquadt). You have the absolute (measurement) error, the relative (measurement) error, the population/sample standard ...
1
vote
1answer
51 views

Why does the rule for multiplication/division take into consideration the no. of significant figures?

I've learned that the rule for multiplication, when taking into account the significant figures, is as follows: The final result should retain as many significant figures as there are in the original ...
0
votes
1answer
107 views

Error propagation from frequency to wavelength

I have measured a value for a frequency of $1.07 \times 10^{10} \pm 5 \times 10^7) \text{ Hz}$. Obviously it is very simple to find the wavelength from this frequency value, which I have (using ...
0
votes
1answer
32 views

Uncertainty in $T$ from measuring $nT$

Suppose I wish to obtain the period of an oscillation, $T$, so I measure the time for $n$ oscillations to obtain $nT$. Suppose I use a stopwatch, so the quantity $nT$ has an uncertainty of around 0.1 ...
1
vote
1answer
87 views

Is there uncertainity of position of the perfectly homogenous radiating body?

I heard the standard interpretation of Heisenberg Uncertainty Principle: Just the measurement affects the position of the body because always you want to see a body (=to measure the position), you ...
2
votes
1answer
50 views

Energy resolution of LHC Electromagnetic Calorimeter

So I am trying to get an estimate of the electromagnetic calorimeter resolution at LHCb, and I have found this online: But I have no idea of what it means. Can anyone explain what the last part ...
0
votes
1answer
63 views

Resolution of experiment is lower than the detector, so how to weigh the data?

I am attempting to create an atomic model based on data from a transmission electron microscope (TEM). Basically you shoot electrons at bunch of identical molecules stuck to a grid, and look at the ...
1
vote
2answers
108 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 ...
1
vote
1answer
75 views

Error in standard deviation and variance from error in data

I have a set of datapoints $x_i$ which have known upper bounds for absolute errors $\delta x_i$. (To clarify, this means each $x_i$ is actually $x_{i_0} \pm \delta x_i$). For simplicity, assume that ...
0
votes
1answer
104 views

How should I calculate uncertainty of measurement calculated as average of two measurements

I am measuring force with two channel transducer. Both channels (separately) of this transducer has been calibrated and I can calculate uncertainty of measurement for each of it. However I want to ...
1
vote
2answers
327 views

Percent error calculations dilemma

I have a set of experimental results for calculating g: 9.82 9.52 10.77 10.39 9.75 9.79 10.13 10.56 10.26 9.84 10.07 9.58 These were taken using a pendulum experiment. My dilemma is that, ...
1
vote
1answer
272 views

What is logical way to calculate percentage error?

I wish to know logic behind percentage error formula. Say, $A$ is measured or calculated quantity, $B$ is theoretical or known or benchmark quantity. Then, what should be the formula for percentage ...