Question

Why does the frequency does not change during refraction as wavelength and velocity changes?

Answer 1

Imagine you produce a wave with in air by using a piston, which you move back and forward at a certain frequency. The wave you produce will be characterized by that frequency, which is determined by the mechanical movement you transmit to the piston. So even if the wave faces a change of media, the pulses you gave remain the same, and so the frequency also remain the same.