Use your units . . . "period" is time, so you know that you have to
set up your fraction with time in the numerator.
10 seconds / 4 waves =
(10/4) sec/wave = 2.5 seconds per wave.
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Notice how the first answer set it up exactly backwards.
He would have seen his mistake immediately if he had
kept the units.
He started out by saying . . . . P = N / t
Keeping the units, P = (waves) / (second)
The answer will have units of "waves per second" .
That's frequency, not period.