How could one can say that frequency spectrum having Nyquist frequency 'x' is the most appropriate representation of a given signal? I have a sinusoidal signal which has  a period of 2 and I want to find the frequencies that are present.I assumed sampling interval as 0.01 and based on this I sampled the signal.The Nyquist frequency i got from this is suppose 'x'.Now if I change my sampling interval to 0.001, Nyquist frequency in this case is '10*x'
So my question is,which frequency spectrum will represent the signal correctly, the one with Nyquist frequency 'x' or the one one with Nyquist frequency '10*x'
The most important thing is to sample at more than twice your signal's bandwidth; the period is largely irrelevant. Say your signal with period 2 is a square wave -- its bandwidth is infinite and you'll never be able to sample it correctly (at least in theory). If your signal is a sine wave, then a period of 2 means its bandwidth is 0.5 and you'll easily sample it adequately.

Personally, whenever possible, I'd sample:


a bit above Nyquist (say, at $2.2B$, where $B$ is the signal bandwidth), to maximize the number of useful frequency bins, and
for as long as possible, to increase the spectral resolution.