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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Error propagation rounding [duplicate]

hope I am right in this section. I am unsure with error propagation. When calculation the error in a titration, many errors has to be taken into account: Error in Glassware/ Error in Balance/ Error ...
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2answers
305 views

Use of normal distribution in measurement error theory

When you study an experimental results you assume that normal distribution describe random error, specially in lab courses in K12. Is this true for every random component error treatment in physics? ...
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1answer
162 views

Error propagation with dependent variables

Based on Microdosimetry theory, trying to figure out error propagation for a lot of quantities that are produced from radiation spectra where each channel with $f(y)$ counts has error $\sqrt{f(y)}$. ...
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1answer
39 views

Residuals are normally distributed

I did not know whether to post this question in the Physics or Statistics section of StackExchange, but the question involves the application of statistics to the analysis of experimental results. I ...
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1answer
38 views

Confirmation of Uncertainty in Indices New Formula? [closed]

I am experimenting relations with regards of the value with uncertainty raised to the $n$th power. I came up with this formula: $$(A\pm\alpha)^n=A^n\pm(A^{n-1}n\alpha)$$ Anyone here able to ...
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0answers
185 views

Calculating accuracy, error, full scale error, relative error and more in a specific case

I recently bought a O2(oxygen) sensor and I am trying to figure out the error in the percentage O2 (O2pct, unitless but in %) output value that it gives out. This error is not stated in its data ...
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1answer
72 views

Error in total counts

I'm performing a radioactivity experiment where I measure a specific number of counts in some time period t. Later on I take the total count rate. (Number of counts/time: $N/t$) I'm supposed to find ...
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1answer
155 views

Inaccuracy at measuring gravity constant with Cavendish experiment

For a scientific work for school I decided to measure the gravity constant with the Cavendish experiment. I set up a structure like the one suggested on this website: ...
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3answers
778 views

What does it mean to “bin” in a spectroscopy context

In the following online article http://www.star.le.ac.uk/~sav2/stats/a.html I see the word "bin" used, in relation to x-ray spectroscopy, both as a verb and as a noun (people both "bin" things and ...
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2answers
37 views

Filament lamp $(V,i)$ behavior between 0 and 1V

I was wondering why the behavior is more "chaotic" at 0~1V when compared to 2V+ (which is when it starts to glow).
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1answer
45 views

Error Propagation for Bound Variables

Say I'm trying to calculate the energy term Pressure*Volume based on measurement of P and V over many different trials. Given a constant temperature, pressure and volume are bound variables as PV=nRT ...
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1answer
169 views

Mass loss for Fusion energy? [closed]

I am thinking how you can estimate the mass loss of the fusion energy for 1 kWh. I think you cannot use Einstein's $E=mc^2$ to calculate the mass loss in the fusion reaction of the Sun. How can ...
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1answer
75 views

Why is drag neglected while dealing with kinematic problems?

Why is drag neglected while dealing with kinematic problems? While dealing with problems related to finding velocity, acceleration and other kinematic problems, it is mentioned to "neglect drag". ...
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0answers
51 views

Error propagation for products [duplicate]

Suppose you have two measured (independent) physical quantities $x$ and $y$ with relative errors $r_x := \frac{\delta x}{x}$ and $r_y := \frac{\delta y}{y}$, where $\delta x$ and $\delta y$ are the ...
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1answer
138 views

Error propagation for exponents

I was told that since $x^n = x\cdot x\cdot x \cdot \ldots \cdot x$ that the error is $$\delta f = f_{\text{best}} |n|\lbrace \frac {\delta_x}{f_{\text{best}}} \rbrace$$ where $f$ is a function of ...
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2answers
41 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 ...
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0answers
36 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
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1answer
47 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 ...
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3answers
421 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
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3answers
78 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
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2answers
974 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 ...
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3answers
90 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?
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0answers
68 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 ...
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0answers
43 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 ...
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2answers
387 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 ...
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5answers
1k 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 ...
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4answers
69 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 ...
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0answers
62 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 ...
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1answer
103 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 ...
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1answer
80 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
45 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
42 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
26 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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3answers
3k 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 ...
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1answer
69 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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0answers
95 views

Eclipse of the sun - Intriguing luminosity curve

I've just recorded the luminosity during the sun eclipse, here is the resulting curve : Only green curve is relevant, blue curve should be ignored (it's actually the temperature). The sky was ...
6
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2answers
240 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 = ...
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2answers
238 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
113 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 = ...
3
votes
2answers
192 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 ...
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3answers
674 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
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1answer
248 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
37 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
231 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 ...
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2answers
996 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 ...
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5answers
572 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
450 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
207 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
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2answers
106 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
84 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 ...