# Nyquist theorem, sample meaning

Given that this wave was sampled at a sampling frequency f:

Why does the wave sampled at a sampling frequency 3f/2 look like this?

What does 3f/2 mean? Does it mean that we sample every 2 waves 3 times?

The sampling frequency is the number of times per second that you measure the particle's position. In the first diagram, the measurements all happen when the particle is in the same place so sampling at that particular frequency causes you to believe that the particle isn't moving at all (the orange line). In the second diagram, we're sampling $$3/2=1.5$$ times more often so, now we see the particle in different positions and, in particular, we see that it's not stationary.
Both $$f$$ and $$3f/2$$ are frequencies, measured in units of $$\mathit{time}^{-1}$$. Sampling at frequency $$f$$ means sampling every $$1/f$$ time units. If you're sampling with frequency $$3f/2$$, you're sampling $$3/2$$ times more than when sampling with frequency $$f$$ for the same time duration.