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

1. Sep 5, 2014

### merrypark3

1. The problem statement, all variables and given/known data

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

2. Relevant equations

3. 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?

2. Sep 5, 2014

3. Sep 6, 2014

### Staff: 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).

4. Sep 6, 2014

### voko

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.