Wave with no wavelength?

A wavefront slows down when it enters into a second medium, the wavefront that followed, which is still in the first medium, still travels at a faster speed. Thus the second wavefront will catch up with the first one, thus shortening the separation between them. This phenomenon is manifested as a shortening of wavelength of the wave.
Since shortening of wavelength is due to the difference in speed of the wave in the two media, the frequency of the wave is unaffected. Unless the speed of the first wavefront that enters into the second medium drops instantly to zero, which is physically impossible as no wave will exist with zero velocity, the wavefront behind will never catch up with the first one.