Question

Natural frequency of the sloshing water in a swimming pool of a cruiser ship is studied by an experimental set up with a scale of 1/10. If the natural frequency is found 3.5 Hz, then what is the natural frequency for full scale?

Answer 1

time to cross pool = L/v = T
where T is proportional to period or 1/f

so L = k v /f where k is some constant

f = k v/L

now I do not know what you have studied. I hope you know that if wavelength is short compared to depth the speed of the wave is proportional to the square root of its length lambda
v = c L^.5
so
f = k c L^.5 / L
or
f = constant /sqrt L
3.5 = constant /sqrt 1 if L = 1
f = = constant / sqrt (10) if L = 10

3.5/f = sqrt 10/1
f = 3.5 / sqrt 10