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

[merrypark3]

Homework Statement

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

Homework Equations

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,
which increase your error)

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?

 

[Quantum Braket]

I think you inverted something there.

Read through this a bit: http://courses.washington.edu/phys431/propagation_errors_UCh.pdf

Afterwards, ask yourself how repeated trials affects the error.

 

[Borek]

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).

 

[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.