Applying FIR filter to data with different sample rates
Since you mention sampling, you are presumably talking of a digital filter.

The cut-off frequency or half-power frequency of a digital filter is
actually relative to the sampling frequency $f_s$.  If your digital
filter is passing signals in the $1$ kHz to $2$ kHz range when you
feed it a signal sampled at $f_s = 20$ kHz, then the pass band is from
$5\%$ to $10\%$ of $f_s$.  These ratios do not change if
$f_s$ changes to some other value, say $40$ kHz.  The same digital
filter will become a filter with passband $2$ kHz to $4$ kHz without
your having to do anything.