In fluid dynamics, Faraday waves are an interesting phenomenon. Not having a background in fluids, Faraday waves were something I wasn't fully aware of until a student made an accidental discovery. When she was starting to look at vertically shaking a Petri dish of water (inspired by methods of creating oscillons in vertically shaken Petri dishes of granular materials), she noticed patterns of waves on the surface of single drops of water on the oscillator. These are Faraday waves, which can be investigated in a fairly simple experimental setup.
Because the student observed similar waves and phenomena on droplets, and not finding any articles in the literature about formal studies of droplets (past research seemed to be like the university lab linked above - water and other liquids in a container, with boundaries (walls) and a relatively flat, 2-D surface), she decided to pursue it and try and find deviations from 2-D surfaces to a more 3-D, curved surface of a small drop of water. Note that studies like this can also be written up and submitted for publication in teacher journals, where we can offer ideas for classroom demos, labs, inquiry projects, and research projects.
This is a wonderful way to create new, novel research projects. On so many topics and phenomena, look at old experiments, think about the parameters that are relevant to those experiments, and then start thinking about ways of taking different parameters, or combinations of parameters, and thinking about what a new experiment would look like. With Faraday waves, think about other ways of tweaking the more traditional experiments to find new things to look at in slightly different ways. As one suggestion, if a student has access to a 3-D printer, imagine the endless surfaces with different shaped indentations one could make, fill those indentations with small amounts of water or any other liquid, and test to see if Faraday waves are formed, and what their properties are as a function of geometry!
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