# Uncertainty of an oscilloscope frequency, read from the period

• zzzriprip

#### zzzriprip

Homework Statement
Uncertainty for lab reports
Relevant Equations
T = 1/f
Hi, I am unsure of what uncertainty to get, so here is my full question: I used the CRO for an experiment, and since what I need is frequency, I read the period, so for the uncertainty of the period, it is the smallest division divided by two. So if my uncertainty for period is 0.001s, then what would be the uncertainty of the frequency? Do I need to use error propagation?

Yes you do, but that is always true. So how do you approach this one?

Yes you do, but that is always true. So how do you approach this one?
Is it considered as a polynomial function? since f = 1/T, so f = t^-1, thus df/dt = -1/t^2, and then do I just substitute t=0.001 into the equation to get the uncertainty?

thus df/dt = -1/t^2
Right.
do I just substitute t=0.001 into the equation to get the uncertainty?
No.
##\Delta f=\frac{df}{dt}\Delta t##.
The derivative needs to be evaluated using the value of t measured.

• zzzriprip and Delta2
Is it considered as a polynomial function? since f = 1/T, so f = t^-1, thus df/dt = -1/t^2, and then do I just substitute t=0.001 into the equation to get the uncertainty?
As @haruspex points out the 0.001s is Δt and you need to also put in t. If you do a little algebra on your result above you can show for this case the percent uncertainty in f will be the same as the percent uncertainty in t (i.e. Δt/t). That makes it easy to understand and use.

• zzzriprip and Delta2