Firstly, the speed. Let's say you are in space and there is light. The light is energy, here considered as a wave. There is vacuum in space, so there's no particles to slow down the light. In the atmosphere, there are air molecules which can slow down the light, though very little. In glass, there is more particles, so the speed decreases yet more. This is why you have refraction of light in glass.
Do you know that formula?
As v, speed, decreases, either f or lambda will decrease. F is the frequency and lambda the wavelength. What I was told is that frequency remains the same, so the wavelength will decrease.
The concept that waves have the same wavelength came from the fact that water waves have the same frequency both in deep and shallow water, where their speed is different.
Hope it helped:)!