In a sampled system all the frequency calculations are inherently really outputting a fraction of the sample rate....
Thus the core of the maths is in your example coming up with a result of 1/8th, which when multiplied by 8K, gives 1K and when multiplied by 16K gives 2K.
The system is measuring in terms of the sample rate, therefore if you want an output in any other terms you must know the same rate.
There are also cases where the sampled data is not a time series of course in which case the sampling might be in terms of distance or radians or something.
Regards, Dan.