Calculating Wave Amplitude & Wavelength in Water Pools

[jsurow]

TL;DR Summary

How would we model/calculate the circular waves in a pool of water (wavelength and amplitude) from a mass falling into it from a given height, and from a fountain of water falling into it continuously?

How would we model/calculate the circular waves in a pool of water (wavelength and amplitude) from a mass falling into it from a given height, and from a fountain of water falling into it continuously?

Is there is a way to describe the initial configuration of the wave based on the stimulus. For example, what is the resultant wave amplitude and wavelength from a X kilogram solid sphere at a velocity of Y meters persecond hitting a Z square centimeter area of water, versus the stimulus being a single sphere of water contacting the same area of surface at a similar speed, versus a continuous stream of water as in a fountain hitting the water.

I'm guessing that the resultant wave is dependent on the energy of the object that hits the water surface, modified by some characteristic of the incident object and also of the ppol of liquid(water) that it falls into, such as its shape, viscosity, surface tension, perhaps even refractive index.

 

[tech99]

Maybe we can find a part analogy with the case of discharging a capacitor into a transmission line. Here the energy of the capacitor is transferred into a wave which travels away from it. I think that the capacitor discharges into the characteristic resistance (impedance) of the line, and the product CR will determine the time for the discharge to happen and the duration of the first half wave. So for a mass falling into water, maybe the energy is converted into a wave, and travels away from the centre. The energy is now spreading out over a plane 2D surface, so the energy density will decrease in proportion to distance, and the amplitude will decrease with the square root of distance.
As Lord Kelvin mentioned, water waves are not straightforward things to study.

 

[Baluncore]

Welcome to PF.

The ripples that spread out across the surface are gravity waves.
https://en.wikipedia.org/wiki/Gravity_wave

Where a continuous stream of water penetrates a water surface, the surface is dragged down by the viscosity shear in the boundary layer of the water. Once the system is stable, no more gravity waves will be radiated.

 

[berkeman]

His areas of research are perhaps a little different, but I'll page @Dr. Courtney to see if he has worked with gravity waves in his impulse research...