Question

The number of cycles that pass through a wave over a given amount of time is the wave's _____.

Answer 1

Frequency.

I would like to elaborate but I think the English meaning of frequency makes it self explanatory.

Period is the time it takes for the wave to complete 1 cycle.
The relation between frequency and period is:
\[f=\frac{1}{T}\]
1 is chosen because we usually take the time to be 1 second. So frequency is usually defined as the number of complete cycles in 1 second.