The period of the wave is the amount of time it takes for a point on the curve to trace a path along this curve and come back to the same height value. The given plot places a passenger 15 ft above the ground at the start. A little less than a minute later, the passenger returns to the initial height.
In the total 15 min of operation, the Ferris wheel completes 22 whole loops (count the distinct peaks of the curve) and 1 half loop, and at the 15 min mark the passenger is stuck at the top. This tells us the unit rate, the number of loops that are completed per minute:
(22.5 loops) / (15 min) = (1.5 loops) / (1 min)
and we scale this rate to find out how much time is needed for one complete loop:
(1.5 loops) / (1 min) = (1 loop) / (1/1.5 min) ≈ (1 loop) / (2/3 min)
So the period is 2/3 of a minute, or 40 seconds.