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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27 views

What can I say about compatibility between predictions and results?

If I have these theoretical predictions: \begin{align} \omega_{p_1} = 4.5132 \pm 0.0003~\text{rad/s} && \omega_{p_2} = 4.5145 \pm 0.0002~\text{rad/s}\\ \omega_{b_1} = 0.0707 \pm ...
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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. ...
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0answers
25 views

Sum of independent errors [duplicate]

During a physics lab we stumbled upon a little problem. The measuring device was unstable, oscillating between two values. We were told to write down the average with the half-difference between the ...
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1answer
29 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 ...
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1answer
24 views

What is the correct way to handle significant figures when calculating compound uncertainties? [duplicate]

When processing experimental data, and calculating an uncertainty value in multiple steps, should intermediary uncertainties be used to a certain number of significant figures or kept to the full ...
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10answers
266 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 ...
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2answers
41 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 ...
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1answer
46 views

Measuring a fluctuating quantity: Instrument error vs. uncertainty, or both?

Say I am measuring a quantity $x$ in physical system whose true value is approximately sinusoidal in time. I have an instrument to sample this quantity, for which the manufacturer gives an accuracy ...
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1answer
58 views

Error propagation of statistical error

I have a pulse profile (binned photon counts versus phase) of a star, and for each count rate I have its statistical error. I want to calculate the so-called pulsed-fraction ...
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1answer
24 views

Error analysis and how values in references are determined

Question 1:Most science textbooks have appendixes that have a value for some physical property of some object. This includes diameter of electrons, viscosity of fluids, boiling points, etc. My ...
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5answers
69 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 ...
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2answers
70 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 ...
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1answer
62 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 ...
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2answers
125 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 ...
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0answers
57 views

How to measure distances to stars by means of spectroscopic parallaxes?

How to measure distances to stars by means of spectroscopic parallaxes on practice? What is the accuracy of measuring distances using this method compared with distances based on HIPPARCOS ...
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2answers
859 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 ...
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0answers
23 views

How to estimate a final error when you have N experiments with N errors? [duplicate]

if we have Xo±e1, X1±e2, X2±e3, ..., Xn±en when we know these, what is going to be our estimation for X, and it's error? for example if we have 344±1, 350±2, 345±5, 338 ± 2 estimation? error of ...
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3answers
81 views

Error propagation estimations for sine and cosine

My lab manual gives this: $B$ is a function of $A$, Greek are uncertainties... $$B + \beta = \sin(A + \alpha) = \sin(A)\cdot\cos(\alpha) + \sin(\alpha)\cdot\cos(A)$$ --> because $\alpha$ is ...
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3answers
122 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?
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1answer
105 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
46 views

Error conversion [closed]

$\alpha_L = \frac{1}{a}\frac{da}{dT}$ 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
512 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 ...
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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 ...
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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?
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1answer
65 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 ...
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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 ...
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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 ...
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1answer
145 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 ...
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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 ...
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3answers
487 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
77 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
85 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
131 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 ...
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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 ...
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3answers
239 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
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
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1answer
557 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
154 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
125 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
46 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
214 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
55 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
64 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
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 ...
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1answer
74 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
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 ...
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1answer
206 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 - ...
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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 ...
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3answers
173 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 ...