Wave structures on a jet entering the bulk liquid

40. Wave structures on a jet entering the bulk liquid

Find an equation between wavelength and jet speed. In article(PDF), this is for two different surface tensions of liquids. But in this problem, water from tube hits the bulk water surface, then on liquid column, there is capillary wave. Like the picture 1. And PDF file is a suggested article from professor.
You need to write down theory(it’s very important) and equation (need detail analysis process) and draw image to show.
(You will possibly use some Laplace transform, differential function or dimensionless variable(form).
You could write by hand and them take photo for me.

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