Why can't frequency of an electromagnetic wave change?

[some_letters]

I understand the relationship between velocity and wavelength when the refractive index changes but I can't fully understand why frequency cannot change. What would happen if it did? why can't the speed of light stay constant as frequency and wavelength change to keep it. Is it because of experiments that we know it is constant?

I want a better understanding of why it cannot change.

 

[ehild]

You can accept that it follows from experiment. But you can also imagine that an incoming wave forces the particles of matter at the interface vibrate at the same rate as its frequency. These vibration of the particles next to the interface force the neighbouring particles to vibrate and so the wave travels in the matter, with the same frequency as the incoming one.

ehild