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Anjish

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**TL;DR Summary:**A fluid on a vertically vibrating plate will, upon reaching a certain frequency and acceleration, produce standing waves on its surface. These are called Faraday waves, first described by Michael Faraday in 1831. Faraday waves are still an active area of research today, more than 150 years after their initial discovery. In current research the terms “Faraday instability” and “standing gravity waves” are also used for this phenomenon.

Please help me understand the relation of the critical frequency with the resonant frequency of Faraday waves to exist in a container filled with liquid like water. How can we calculate it mathematically?

IF I want to investigate it by changing the viscosity, depth of the liquid and temperature and how it affects the amplitude and critical frequency of the Faraday waves, if there is no mathematical equation, can we deduce one? can there be a relationship? and also can anyone suggest more relations or investigations I can take with faraday waves?

I am little confused with existing literature and the physics of faraday waves, especially the mathematics of it if it exists. Please help me. This is my current research question

"How do variations in the viscosity of the liquid (or different liquids) and changes in the temperature of the vessel affect the wavelength, amplitude, and frequency of Faraday waves?"

Is it valid? IF yes can you help me with the methodology part and physics and mathematics part of it? what is the maths I can use or formulas to calculate? Is water propagation and dispersion relevant? Can this science be used- https://en.wikipedia.org/wiki/Dispe...e table below, the,the phase and group speeds.

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