# Tagged Questions

246 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 ...
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### 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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### 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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### 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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### 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& ...
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### 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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### 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, ...
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### 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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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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?