What happens if I sample at 512hz and the signal is 500Hz?

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You can’t sample 500 Hz with 512 Hz. Instead your samples will end up producing an alias at 12 Hz.

This diagram shows what happens. The sample points are the dotted lines, at a frequency of fs. The signal being sampled is the black sinewave fa. But the resulting samples actually describe the red sinewave fs — fa. This false result is said to be an ‘alias’ of the real signal, fa.

But note that its frequency is only related to the original by the arbitrary sampling rate — it has no harmonic connection. Also, once these samples are in there, they’re in there — there’s no way to distinguish them from ‘real’samples. The lack of a harmonic relation and the fact that once there you’re stuck with it means that this is a very bad thing to let happen.

To prevent this, it is imperative that a filter is used in the signal path to remove all frequencies above half of the sampling frequency.