The sampling frequency needs to be higher than 2 * signal frequency.
* Signal 1kHz, sampling frequency 2kHz --> no meaningful results
* Signal 1kHz, sampling frequency 2001Hz --> you need to perform an RMS calculation over 2000 samples to get meaningful result
* Signal 1kHz, sampling frequency 2010Hz -->you need to perform an RMS calculation over 200 samples to get meaningful result
If you´re interested in frequencies up to 1kHz you may use 3kHz sampling frequency. So far so good.
(only 3 samples are sufficient to perfectly reproduce the 1kHz amplitude)
But you additionally need to suppress all frequencies above 1500Hz in a way that their amplitudes are very low.
All frequencies above 1500Hz will create alias frequencies with the same amplitude as the original frequencies.
Example: Original 2500Hz, 0.1V amplitude will cause an alias frequency of 500Hz with 0.1V amplitude.
Thus you need to suppress this 2500Hz signal.