Why the frequency in both shallower and deeper part is the same?

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SUMMARY

The discussion centers on the phenomenon of wave behavior in water, specifically addressing why the frequency of waves remains constant in both shallower and deeper regions. It is established that while the wavelength decreases in shallower water, the frequency remains unchanged, indicating no energy gain or loss at the boundary. This conclusion is supported by Maxwell's equations, which require the electric field to be continuous across boundaries, thereby necessitating a constant frequency.

PREREQUISITES
  • Understanding of wave mechanics and properties
  • Familiarity with Maxwell's equations in optical media
  • Basic knowledge of wave refraction
  • Concept of energy proportionality to frequency in wave physics
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  • Explore Maxwell's equations and their implications in wave behavior
  • Investigate the relationship between wavelength, frequency, and energy in waves
  • Examine case studies of wave interactions at boundaries in various fluids
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Physicists, engineering students, and anyone interested in wave dynamics and optical physics will benefit from this discussion.

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Use water waves as examples.
Put something in the water. When you produce a wave, refraction will occur on above the 'something'.
But why the frequency in both shallower and deeper part is the same?
In addition, the wavelength in the shallower part reduce. Does this means the engery of the wave increase?
 
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The energy of the photons that comprise the wave is proportional to their frequency. If there were a frequency change at an interface, this would mean energy is being gained or lost at the boundary. Since this is not observed to happen, we conclude that the frequency does not change.

A more quantitative reason is imposed by Maxwell's equations. Maxwell's equations in optical media demand that the electric field be continuous over the boundary for all time. This is only possible if the frequency of the wave does not change.

Claude.
 

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