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

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The discussion focuses on why the frequency of water waves remains constant in both shallower and deeper areas despite changes in wavelength. It explains that when a wave is produced, refraction occurs, but the frequency remains unchanged to prevent energy loss or gain at the boundary. The relationship between wave energy and frequency is highlighted, noting that energy is proportional to frequency, which supports the conclusion of constant frequency. Additionally, Maxwell's equations dictate that the electric field must be continuous across boundaries, further enforcing the idea that frequency does not change. This understanding is crucial for comprehending wave behavior in different depths of water.
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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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