Capillary waves - surface standing

[antknee]

With capillary waves I need to calculate where surface standing waves will occur.


Assume mediums are pure water and air.
Assume the capillary waves are bounded in a box such that the wavelength matches the height of the water and width/length of the box.
Assume effects of gravity and interference are neglible.
Assume the box is vibrated sinusoidally from the bottom at a frequency of 100KHz.


The standing waves will appear on the surface of the water in a triangular lattice (I believe). But what distance between nodes? I am too long in the tooth to do the calculations myself, so any pointers, websites, resources, thoughts would be welcome.

 

[Valerie Park]

The distance between nodes will be equal to the wavelength of the wave. To calculate this, you can use the formula v = fλ, where v is the wave speed, f is the frequency, and λ is the wavelength. In this case, the wave speed is equal to the speed of sound in water (1480 m/s). Therefore, the distance between nodes will be 14.8 cm.

 

[sir-pinski]

To calculate where surface standing waves will occur in a capillary wave system, we must first understand the properties of capillary waves and how they interact with their environment. Capillary waves are small ripples that form on the surface of a liquid due to surface tension forces. They are typically created when a liquid is disturbed by wind or other external forces. In this case, we are assuming that the medium is pure water and air, and the capillary waves are bounded in a box with dimensions that match the wavelength and height of the water.

To determine where standing waves will occur, we must first consider the effects of gravity and interference. In this scenario, we are assuming that these effects are negligible, which means that the standing waves will be evenly spaced and have a consistent wavelength. Next, we must consider the frequency at which the box is being vibrated. In this case, it is vibrating at a frequency of 100KHz.

To calculate the distance between nodes in the standing waves, we can use the formula for the wavelength of a standing wave on a string: λ = 2L/n, where λ is the wavelength, L is the length of the string, and n is the number of nodes. In this case, the string is the surface of the water in the box and the length is equal to the width or length of the box.

Since we are assuming that the wavelength matches the height of the water, we can use the formula for the wavelength of a capillary wave: λ = 4π√(T/ρg), where T is the surface tension, ρ is the density of the liquid, and g is the acceleration due to gravity. By combining these two formulas, we can calculate the distance between nodes in the standing waves on the surface of the water.

As for resources and websites, there are many online calculators and formulas available that can help with these calculations. Additionally, textbooks and research papers on fluid dynamics and capillary waves may also provide helpful information. It may also be beneficial to consult with a physics or engineering expert for further guidance and assistance.