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What does $rm fT/Hz^{0.5}$ mean?

Physics Asked by Tbw on September 25, 2021

I was browsing the Wikipedia page for "Magnometer" and saw the figure that a caesium vapour magnetometer has a sensitivity of $300 rm fT/Hz^{0.5}.$ I understand femtotesla but I am confused about the meaning of square root hertz and the what the overall unit is truly measuring. I saw this post about square roots of units, but it gave no examples.

One Answer

Measurements are noisy. They are less noisy if you measure slowly, for reasons that are related to the Poisson distribution of uncorrelated random events. If that fundamental statistical noise is your primary source of fluctuations in your measurement, its precision will vary like $sqrt t$, where $t$ is the duration of the measurement.

If you sample a noisy signal ten times per second, you can use longer samples than if you are sampling a thousand times per second. So if you run the same detector at 10 Hz, you should expect it to be less noisy than at 1000 Hz --- by a factor of ten, because of the Poisson nature of uncorrelated errors. The $rm Hz^{0.5}$ in the denominator of your error coefficient tells you the uncertainty will be proportional to the square root of the measurement frequency.

Correct answer by rob on September 25, 2021

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