a man lying on a air matress in the ocean rises and falls through 1 complete cycle every 5 s?

Question

the crests of the waves causing the motion are 20 m apart
dtermine
the frequency of the wave
the speed of the wave

Answer 1

So the wavelength is 20m
and it takes 5 seconds for a full cycle
(which means 12 cycles per minute).

The frequency is 0.2 Hertz (which is the same as 1/5 cps or 12 cycles/minute).

The speed is 20m per 5s, or 4 m/s.

(Of course, this assumes a "closed system"
with no other unmentioned forces or factors.
It ignores not only the wind blowing on the mattress,
but also the slippage of the mattress on the water's surface,
as affected by the coefficient of friction, etc.
And it also ignores which way the shark is pushing it from below,
and how fast the guy is paddling to get to shore.)

Answer 2

The wave equation is

frequency * wavelength = velocity

The wavelength is given as 20 m.
The frequency is 1 cycle / 5 seconds.
Now solve for wavelength.

Answer 3

speed = 4 m/s

frequency is 1/5 cycles per second = 0.2 s^-1
(or 0.2 of that useless "Hertz" unit).