Subject: Is the fundamental characteristic of waves the wave length or frequency

1. Since a radiation changes its speed in different materials, 
either the wave length or the frequency (or both) have to change 
too. Which of them - if any - stays unchanged, being in this 
sense a "more fundamental" characteristik of the radiation than 
the other?
2. If a radiation travels with light speed (or almost with that) 
and the particle - photon, f.e. - "makes" waves, does the 
particle move in effect faster than the radiation itself, or is 
the concept of "wave" only a vehicel of understanding and not a 
"real" wave in the sense the particel has to travel along?

Re: Is the fundamental characteristic of waves the wave length or frequency