All Questions

0
votes
1answer
73 views

Problem in measuring uncertainty

While performing an experiment involving a bar pendulum, we had to measure the time period of one oscillation by measuring the time taken for 30 oscillations. There is some confusion regarding ...
0
votes
1answer
136 views

Why does taking more readings reduce random error? [closed]

So I was tossing a coin And I did two experiments Experiment 1: Tossing same Coin with no fan with different torque each time and did'nt much care about orientation of the coin, 8 times I got 5 ...
0
votes
1answer
50 views

Adding uncertainties when you cannot make any assumptions about the measurements [duplicate]

From what I read, when adding two $x$ and $y$ measurements with uncertainties $\delta x$ and $\delta y$, the resulting uncertainty is determined by doing: $$\delta z = \sqrt{(\delta x)^2 + (\delta y)^...
0
votes
1answer
115 views

What's the meaning of the $\sigma$'s of a particle physics measurement?

In particle physics experiments, one often quotes the result of measurement of an observable with $1\sigma$, $2\sigma$, $3\sigma$ ranges. The experiments typically give a best-fit value with a $3\...
-1
votes
1answer
184 views

Fractional uncertainty question

Q. A ball falls freely from rest with an acceleration g. The variation with time t of its displacement s is given by s = 1/2 gt^2. The percentage uncertainty in the value of t is ±3% and that in the ...
0
votes
1answer
118 views

Smallest uncertainty ever achieved in position measurement in QM?

The Heisenberg uncertainty principle states that $$\Delta x\Delta y\geq\hbar/2$$ Since the magnitude of $\hbar$ is $10^{-34}$ we could measure both $x$ and $p$ with an uncertainty magnitude of $10^{-...
1
vote
2answers
67 views

A doubt related to Significant Digits

Could someone please explain this statement to me "Reporting the result of measurement that includes more digits than significant digits is superfluous and also misleading since it would give a ...
0
votes
2answers
231 views

How the last digit in significant figures is considered doubtful?

If a reading of a length on meter rod is 44.6cm with least count of 1mm And last point of the length is exactly on 44.6 not in between of 44.6 or 44.7 Then how is it doubtful?
2
votes
2answers
102 views

Simple question about propagation of error/uncertainty

I'm stuck on a seemingly simple question about propagation of error. Say we repeatedly measure the speed of a particle, and we estimate the uncertainty in the measured speed to be 10 percent. What is ...
1
vote
1answer
41 views

Measurement of decay rates and statistics

During my nuclear physics lab I was measuring decay rates of Fe59. The average was around 20 decays per second. But I did two series - in one I was measuring number of decays per 90 seconds and in the ...
0
votes
2answers
110 views

Probability of Obtaining a Certain Value (normal distribution)

In my textbook it says that the probability of obtaining a value (which its Gauss distribution is known) is simply ($\frac{1}{\sqrt{2\pi }}$ * $e^{\frac{(x_{1}-X)^{2}}{2\sigma ^{2}}}$ dx ) where $x_{...
0
votes
1answer
459 views

Standard deviation as uncertainty of a single measurement

If we have made the following several measurements of the quantity x that follow a normal distribution: 86, 85, 84, 89, 85, 89, 87, 85, 82, 85 The mean is 85.7 and the standard deviation(std) is ...
1
vote
1answer
105 views

Question when comparing two experimental results

In my textbook it says that if two experimental results vary less than 3$\sigma$ then they can be considered to have arrived at the same result. My question is how do you determine this "x$\sigma$". ...
0
votes
2answers
120 views

Why do scientists do particle collision experiments more than once?

Why are the particle collision experiments involving the same particles are done more than once. Shouldn't the collision of the same particles with the same velocity as the experiment before give out ...
1
vote
1answer
84 views

Measuring through meter scale

What if the measuring thing is found to have length between 6mm and 7mm. Like u r measuring the length of an object which has the length between 5.6cm and 5.7 cm. The millimeter distance was between ...
3
votes
0answers
45 views

Continuous Measurement equations

In a physics text, "Quantum Measurement Theory and it's Applications" by Kurt Jacobs, it describes the idea of a "continuous measurement" (measurement taking place over time $T$): $$dy = x_{true}dt + \...
2
votes
3answers
1k views

Propagation of uncertainty in integral formula

I have a moving object with mass $M$ whose 1D trajectory $x$ can be tracked and known over time with a certain sampling rate (EDIT: to make it clear, I don't have the analytical form of $x$, that's a ...
-2
votes
1answer
32 views

How to get second-order equation from 2 first-order equations with the same dependent variable?

I have a current sensor thats returns an output in voltage (Ts) dependent on the current that passes throught the inputs (I) and the voltage feed input (Ta). I built a table and measured the Ts, while ...
1
vote
1answer
42 views

Assigning distributions to the result of measurements

In my data analysis course we were taught that whenever we perform a measurement, the measured value is to be interpreted as the mean of the distribution for the true value. And the error in ...
1
vote
1answer
43 views

Covariance when two parameters have relative scaling error

I was reading error propagation from "Introduction to Statistics and Data Analysis for Physicists" by G. Bohm and G. Zech, and I stumbled upon this example, Given are the sides a, b with a reading ...
2
votes
2answers
43 views

Replacing '< x' by a defined value [closed]

I do have a dataset containing nearly a decade of particulate matter measurements. At the lower precision limit of the measuring instrument, there are values given like ...
3
votes
1answer
150 views

A question about error analysis, please help?

So in class we are doing an experiment on the period of a pendulum where you measure the period of oscillation with a stopwatch. Now the way the lab manual shows how to do the error analysis is by ...
1
vote
3answers
58 views

When analyzing data from an experiment, is each $x_i$ a random variable?

When we perform one experiment we have to measure several quantities and take some number of measurements for each of them. Those quantities can be things like positions, instants of time, and so ...
3
votes
1answer
271 views

Why do we divide the standard deviation by $\sqrt{n}$? [duplicate]

I've been studying experimental physics on the book "The art of experimental physics" and on the chapter about error analysis there's something that has been bothering me. The author says: Now that ...
4
votes
2answers
204 views

Combining two data points with different uncertainties

I have two separate algorithms (call them "A1" and "A2") which reconstruct the $(x, y)$-position of an event in a particle detector. I can test both of these algorithms on simulated events from a very ...
4
votes
0answers
635 views

Calculating statistical significance of peak over background in counting experiment

I histogrammed the invariant masses of particular events in a counting experiment. There is a specific peak which towers over the expected exponential background. How can I give the statistical ...
1
vote
1answer
583 views

How to find the error of all the counts within the Full Width Half Maximum (FWHM)?

We've been doing Gamma ray spectroscopy and have peaks from various sources. We'd use Poisson statistics, but obviously the detector doesn't have a resolution of zero, thus we are summing the counts ...
0
votes
1answer
175 views

Combining errors. Gamma spectrometry, Poisson distribution

I have run an experiment 3 times and measured the results by gamma spectrometry. For example I get values like this (1 $\sigma$): $100 (10)$ $90 (8)$ $110 (12)$ The above 1 sigma error is based ...
3
votes
1answer
297 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
341 views

Uncertainty of approximately sinusoidal voltage measurement

Say one is interested in measuring the mean value an approximately sinusoidal voltage with an instrument that has an accuracy of 0.01 V, according to its spec sheet. 10 periods of the oscillation have ...
2
votes
5answers
287 views

What's the difference between $10\%$ of $10\text{ cm}$ and $1\text{ cm}$?

I overhead a physics professor at my university on the phone: I interviewed that student you sent me, but he didn't know the difference between increasing the length of a $10\text{ cm}$ rod by $1\...
1
vote
0answers
80 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 0.0003~\text{...
11
votes
10answers
584 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 ...
1
vote
1answer
293 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 ...
1
vote
0answers
61 views

Weighted average whenever a variance is 0? [closed]

So I have data for the number of times a certain event happens. Each column is a different event and each row is one trial. A sample of data would look like \begin{bmatrix} 1& 4& 7& 6&...
2
votes
2answers
702 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?
3
votes
1answer
181 views

Time of Measurement Vs Number of Measurements

Let's say that an experiment has to determine the number of cosmic muon at sea level. The appropriate equipment is ready to measure the counting rate. I can think of two ways Count for 10 minutes, ...
-1
votes
1answer
203 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?
7
votes
4answers
9k views

Averaging decibels

Wikipedia: The decibel (dB) is a logarithmic unit that indicates the ratio of a physical quantity (usually power or intensity) relative to a specified or implied reference level. If I measure ...
6
votes
2answers
22k views

How to combine the error of two independent measurements of the same quantity?

I have measured $k_1$ and $k_2$ in two measurements and then I calculated $\Delta k_1$ and $\Delta k_2$. Now I want to calculate $k$ and $\Delta k$. $k$ is just the mean of $k_1$ and $k_2$. I thought ...
4
votes
1answer
1k views

Is $\sigma$ or $\sigma / \sqrt{N}$ is error of a measurement?

I wonder whether $\sigma$ or $\sigma / \sqrt{N}$ is error of a measurement. When I measure, say $0, 1, -1, 1, -1$, I have a $\sigma = 1$. I just measure $0, 1, -1$, I also have $\sigma = 1$. But in ...
13
votes
3answers
23k views

How to combine measurement error with statistic error

We have to measure a period of an oscillation. We are to take the time it takes for 50 oscillations multiple times. I know that I will have a $\Delta t = 0.1 \, \mathrm s$ because of my reaction time....
3
votes
2answers
881 views

Question about uncertainty

Are $3.43\pm 0.04$ $\frac{\mathrm{m}}{\mathrm{s}}$ and $3.48$ $\frac{\mathrm{m}}{\mathrm{s}}$ within expected range of values? The answer is yes, but I do not clearly see why this is so. I appreciate ...
3
votes
3answers
749 views

Calculating uncertainties for a final result

Say you are dividing 2 times with uncertainties: $$\frac{t_1}{t_2} ~=~ \frac{0.551s \pm 0.002s}{ 0.712s \pm 0.002s}.$$ After doing the calculations you get: $$\frac{t_1}{t_2} ~=~ 0.774 \pm \ldots?...
2
votes
2answers
113 views

How to properly read a measurement result if it is a number?

If the result of a measurement is i.e. $3.2 \pm 0.7$, what is 0.7? At which confidence level we know that the real result is inside of this interval?
2
votes
5answers
2k views

Are Uncertainties in Measurements Important?

In the first lecture of MIT's Classical Mechanics Prof. Lewin highlights the importance of uncertainties in measurements by quoting "Any measurements, without the knowledge of uncertainty is ...