Ya know.. you're right. I'm an engineer and also have a DSP textbook up in the attic somewhere. That was a hard freaking class. When i pictured say for example a lumpy sine wave, i was thinking that one sample per half period wouldn't capture the lumps. But of course those lumps are coming from higher frequency sine wave components and so the Nyquist freq would be respective to those higher freq sine waves, not the big lumpy sine wave i was picturing. I forgot that all signals can be constructed by the addition of multiple sine waves of various frequencies. So with this in mind, you just need that highest freq component, and sampling it at double the freq is all the accuracy you need.