Is there a frequency cutoff for Debye theory of capillary waves?

[Shing]

I calculated the energy density of capillary waves with Debye method (pretty much Debye model in 2D), and I assumed there is a frequency cutoff for capillary waves as well. However, when I checked my work with solution I was quite surprised that the solution suggests there is no such a cuttoff!

I have tried so hard to convince myself why; the only way out I can think of is: because capillary waves are visible to naked eye, hence their wavelength is larger than the atom intervals. But it is kind of a lousy try... so why exactly we have no cutoff for Debye theory of capillary waves(ripples of small amplitude and short wavelength on the surface of a liquid)?

 

[eljose79]

Thank you for sharing your findings on the energy density of capillary waves using the Debye method. I understand your surprise at the solution not showing a frequency cutoff for capillary waves. it is important to critically analyze our results and try to understand any discrepancies.

One possible explanation for the lack of a frequency cutoff in the Debye theory of capillary waves is that the model assumes an idealized scenario where the surface tension and gravity are the only forces acting on the liquid surface. In reality, there may be other forces at play, such as wind or surface contamination, which could affect the behavior of capillary waves. These external factors could potentially prevent a frequency cutoff from occurring.

Another factor to consider is that the Debye model is a simplified 2D representation of capillary waves, while in reality, capillary waves exist in a 3D environment. This could also contribute to the lack of a frequency cutoff in the solution.

I would also like to address your suggestion that the wavelength of capillary waves being larger than the atom intervals could be the reason for the absence of a cutoff. While this is a valid point, it is important to note that the Debye model takes into account the wavelength of capillary waves in its calculations. Therefore, even if the wavelength is larger than the atom intervals, it should still be accounted for in the model.

In conclusion, it is always important to question and analyze our results in scientific research. While the Debye theory may not show a frequency cutoff for capillary waves, further studies and experiments could provide a better understanding of the behavior of these waves. Thank you for bringing this topic to our attention and sparking a discussion on the topic.