Shooking the rope up and down 5 times per seconds means that there are 5 cycles of the wave (or 5 crests) in one second, and so its frequency is [tex]f=5 Hz[/tex].
The period T is the reciprocal of the wave's frequency, therefore it is
[tex]T= \frac{1}{5 Hz}=0.20 s [/tex]
