I have measured a value for a frequency of $1.07 \times 10^{10} \pm 5 \times 10^7) \text{ Hz}$. Obviously it is very simple to find the wavelength from this frequency value, which I have (using $c=2.9979 \times 10^8$). However I am lost as to finding the error for the wavelength. The values I keep calculating for the error keep coming out as 2 orders of magnitude or more from the wavelength, which is very counter-intuitive. Please help!


1 Answer 1


if error in wavelength is $\delta \lambda$ and error in frequency is $\delta f$ then

$${\delta f \over f} = {\delta \lambda \over \lambda}$$


$${\delta \lambda } = \lambda {\delta f \over f}$$

The formula above should give you something more reasonable for the error in the wavelength.

More generally if

$$ X=kA^n$$

where k is a perfectly known constant

$$ \delta X= X ~|n|{\delta A \over A}$$


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