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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718 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
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4answers
53 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
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0answers
20 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
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1answer
18 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
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1answer
34 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 ...
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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
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1answer
23 views

A way to treat uncertainty in intensity measurement

I did an experiment to prove the inverse square law but don't know if my idea to calculate the error is correct. The relationship is $I=const*r^{n}$ with n=-2, we had a computer software to read the ...
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0answers
21 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 ...
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0answers
38 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 ...
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0answers
36 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 ...
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0answers
12 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 ...
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2answers
84 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
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1answer
43 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?
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2answers
119 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
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2answers
66 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 ...
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0answers
40 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
63 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
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1answer
88 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
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1answer
23 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
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1answer
155 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
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2answers
98 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
507 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
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1answer
104 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
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1answer
59 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
80 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 ...
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0answers
51 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
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1answer
230 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
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1answer
96 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 ...
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1answer
44 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
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1answer
89 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
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1answer
29 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 ...
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1answer
53 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
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1answer
43 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
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1answer
54 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 ...
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2answers
89 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
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1answer
64 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
85 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
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2answers
236 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
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1answer
222 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 ...
2
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0answers
35 views

Maximum error of number of observations within several certain intervals – Accuracy of variable is known

I have carried out a series of measurements of different thermal comfort parameters from which I have calculated another variable called PMV. My data set consists of hourly measurements (and ...
0
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1answer
43 views

Numerical Error Propagation

I'm doing the common experiment of determining $ g $ by means of a simple pendulum, and I've decided to do so by measuring the period of the pendulum at variable lengths. I've had no problems ...
0
votes
1answer
337 views

Frictionless Cart on a Ramp (Experimental Design Question)

Question: Why is the calculated value for our final velocity higher than our predicted value? Since our prediction neglected air resistance and friction, shouldn't the velocity for the actual cart ...
0
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0answers
62 views

Uncertainty of measurement with goniometer

I got a goniometer with scale -90 to 90 degree. I use only 0 to 90 degree. One section of the scale has 1 degree. I read a value of $62^\circ$. What is the uncertainty of this measurement? I thougt ...
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0answers
28 views

Why can't we use the Neyman-Pearson likelihood ratio directly?

If you have a bunch of events and would like to choose a cut to distinguish background and signal, you can take the likelihood ratio $$ \lambda(\vec x) = \frac{f(\vec x| s)}{f(\vec x| b)} $$ and the ...
0
votes
3answers
51 views

Can a piezo actuator have infinite resolution?

See here: http://www.omega.com/googlebase/product.html?pn=LD400-1&gclid=CjwKEAjw77OhBRCJ7Onfp_HNtwYSJACZqHAWVTfW1BO4RSfSVjz9P3Q4FoPTvZ2r3NIc2W1uEthVhBoCgUHw_wcB I don't think so. Do they just ...
0
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1answer
54 views

How can I find an error formula for density? [closed]

$${p} = \frac{4m}{πtd^2}$$ How can I find the error in this formula? I don't know where to begin. I know that I'm looking for the "partial derivative" of density to solve this, but that is a brand ...
2
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2answers
133 views

How should I quote errors when measurements are asymetrically clustered?

Suppose five people measure the length of a stick and report the following values 4.90cm 4.92cm 4.93cm 4.94cm 4.94cm In high school science we are told that in ...
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1answer
129 views

Error calculation for experimental data

I have the list of experimental values: $$\{w_i \pm \Delta w_i\},$$ where $w_j$ is a mean value and $\Delta w_i$ is an error. I want to calculate the second list $\{a_i \pm \Delta a_i\}$ according to ...
0
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1answer
34 views

Error limits when we have 4 lengths adding up and then finding its mean?

I have the following readings for length of a wire: 10.2 ± 0.1 cm 10.3 ± 0.1 cm 10.1 ± 0.1 cm 10.2 ± 0.1 cm Now, when I find out the mean value, I get: (10.2 ± 0.1 + 10.3 ± 0.1 + 10.1 ± 0.1 + ...
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0answers
44 views

What is the error on measuring the phase of a sine wave?

Let's say I have a wave, with frequency $\omega$ and phase $\phi$, of the form: $$y(t) = 1 + A \sin(\omega t+\phi)$$ where $A < 1$. I have measured this wave N times, and we can assume these ...