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

  1. Sep 5, 2014 #1
    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 [itex]t=T_{1}+T_{2}+\cdots + T_{n}[/itex] (Measuring n cycle)

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


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

    This [itex] \delta T [/itex] is a error for a period.

    Therefore,

    [itex] \delta t= \sqrt{n(\delta T)^{2}}=\sqrt{n} \delta T[/itex]

    But, [itex] \delta t \propto n[/itex] (as n increases, the scale for one div the screen become smaller,
    which increase your error)

    So [itex] \delta t = \sqrt{n} \delta T \propto n [/itex]

    So, [itex] \delta T \propto \sqrt{n} [/itex]


    Therefore, measuring the least number of cycle is best

    Is it correct?
     
  2. jcsd
  3. Sep 5, 2014 #2
  4. Sep 6, 2014 #3

    Borek

    User Avatar

    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).
     
  5. Sep 6, 2014 #4
    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.
     
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