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 propogation MCQ [closed]

This MCQ below recently appeared in an entrance exam. I'm not asking for the solution but just wanted to know if there is any flaw in the steps mentioned below and also if anyone is sure of the answer ...
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0answers
38 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 ...
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1answer
50 views

About $\chi^2_\text{adjusted}$ [closed]

I am reading "An Introduction to Error Analysis: The Study of Uncertainties in Physical Measurements by J. R.Taylor", and I read the following formula in an exercise: ...
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1answer
21 views

Error estimation in peak location determination by centroid method

I am trying to locate peak in a data set by numerically calculating the peak using centroid method. How can I estimate the error associated with this peak determination?
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1answer
30 views

Combining ±% with ±dB in measurement uncertainty

Firstly apologies if this is not the correct place to post this but wasn't sure which site would be good to ask regarding about measurement uncertainty calculation. I am trying to calculate the ...
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0answers
38 views

Background subtraction for a signal ans Errors Analysis

I use a CCD to see the split of a energy level due to Zeeman effect. I have a 1 dimensional CCD of 7926 pixel of 7μm each one. My CCD analyze a region 2 dimensional, and then it steps forward 200 ...
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1answer
30 views

Significant figures in measurement with error

Someone can explain me what's the rule behind the correct expression of a quantity $K$ with its error $\Delta K$ as $K \pm \Delta K$? They must have the same number of significant figures? Or the ...
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1answer
37 views

What is the experimental uncertainty of an ensemble measurement? [duplicate]

Let's say you measure the time it takes for 10 oscillations of a mass undergoing simple harmonic motion to within ± 0.01s, what is the uncertainty of the period of one oscillation?
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3answers
405 views

What limitations are there in measuring physical properties accurately?

In a StackOverflow answer, I attempted to explain why a 32-bit float was perfectly adequate for representing the questioner's weight measurement: Physical properties are inaccurately measured ...
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1answer
118 views

How to find percentage error of equivalent resister? [closed]

The resistors of $R_1=100\pm3Ω $ and $R_2=200\pm4Ω $ are connected in parallel.Then express equivalent resistance with percentage error. I know how tho find percentage error if resistors are ...
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2answers
46 views

Significant error conversion

So here is my question: Say we have measured something to be 15,67 mm and the significant error is $\pm 0,01$mm. then we convert the measurement to meter to be 0,01567m would the significant error ...
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1answer
173 views

Relative error of equivalent resistance of resistors in parallel

I just saw a formula in my book for relative error in equivalent resistance of two resistors connected in parallel. $\frac{\Delta R}{R^2} = \frac{\Delta R_1}{R_1^2}+\frac{\Delta R_2}{R_2^2}$ ...
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1answer
43 views

Significant Figures (rules of addition)

It is a simple one but different teachers answer this question differently. $$34+1.4+0.2$$ what would be its answer with due regards to significant figures?
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2answers
68 views

Calculation of error in focal length? [closed]

$u=-10cm$ $v=10cm$ Using the formula the focal length is 5 cm. But how do I get the fractional error in focal length when neither $\Delta u$ nor $\Delta v$ are specified? The options given are ...
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3answers
99 views

Chaos theory deterministic or non-deterministic?

While i was studying about chaos theory, i stumbled upon this, When a ball confined in a square, and at the center is located a circle, is to bounce elastically, the path of the object deviates ...
1
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1answer
107 views

Why is uncertainty divided by $\sqrt{3}$?

Why do we have to divide uncertainty of the measurement by $\sqrt{3}$? For example we have the uncertainty of the measurement with a ruler being the smallest scale of 0.01cm, and it is not our ...
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2answers
61 views

What's the difference between average absolute error and relative error?

I am quite confused by both these terms. I would like to know what's the exact difference between both these terms and which one is more accurate.
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0answers
32 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
36 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
34 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
30 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
292 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
67 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
74 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
72 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
32 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
80 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
103 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
86 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 ...
2
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2answers
202 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
64 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
1k 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
24 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
110 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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2answers
136 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?
4
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1answer
118 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
49 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
823 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
167 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
69 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
votes
3answers
111 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 ...
2
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1answer
109 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
195 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
133 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
549 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
82 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
96 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
147 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 ...