# How many cycles of time should be measured for the most accurate T?

## Homework Statement

Measuring the period of a sine wave using oscilloscope, for the best accuracy, is it better to measure only one cycle?

## The Attempt at a Solution

Let $t=T_{1}+T_{2}+\cdots + T_{n}$ (Measuring n cycle)

From error propagation formula,
$\delta t = \sqrt{(T_{1})^2+(T_{2})^2+\cdots + (T_{n})^2}$ (or $\delta t= n \delta T_{1}$ ???)

but as $T_{1}, T_{2}, \cdots , T_{n}$ are independent so the value of each $\delta T_{n}$ is same. So, let $\delta T= \delta T_{1} = \delta T_{2}= \cdots = \delta T_{n}$

This $\delta T$ is a error for a period.

Therefore,

$\delta t= \sqrt{n(\delta T)^{2}}=\sqrt{n} \delta T$

But, $\delta t \propto n$ (as n increases, the scale for one div the screen become smaller,

So $\delta t = \sqrt{n} \delta T \propto n$

So, $\delta T \propto \sqrt{n}$

Therefore, measuring the least number of cycle is best

Is it correct?

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Borek
Mentor
Common logic tells me measuring once length of several cycles should yield a better result (as the measurement error is effectively divided by the number of cycles, which in an exact number).

Caveat: if the cycles are not identical, this way you will lose the information about variability (variance).

Measuring multiple cycles gives better accuracy if your clock is accurate. If the clock itself is drifting, then it is a nasty question. I think we need more context here.