No of samples 4mega samples per second,using 8 bit ADC,V p_p is6V. calculate frequency and peak power This place has been great in helping me to understand my online image and signals class!

I've moved on to another question and wanted to see if I'm correctly grasping the subject.  The next question is as follows:


  If we sample a pure sine signal at "sam" samples per second, and there are 8 samples per cycle of the signal, and we have not undersampled the signal, what is the signal's frequency in cycles per second?


So using the Nyquist-Shannon theorem I know I have a Nyquist rate of $8\frac{samples}{cycle}$ so I believe to calculate the signals frequency in cycles per second I need to do the following:

$8\frac{sam}{cycle} = 2\,f_{max}$

$8\frac{sam}{cycle} = 2\left(\frac{sam}{sec}\right)$

$4\frac{sam}{cycle} = \frac{sam}{sec}$

$\frac{sam}{sam}=\frac{1}{4}\frac{cycle}{sec}$
There are sam samples per second and 8 times less pure sine cycles per second. This means that there are sam/8 pure sine cycles per second. 

What shannon has to do with that? Probably you mean that Niquitz allows you to reduce sampling, make it 4 times more rarely, as low as sam/4 samples per second. That would sample twice per sine period.