Wavelength and speed both depend on the material of the medium.
Explanation:
Let denote the frequency of a wave. Let denote the speed of that wave in a given medium. Let denote the wavelength of that wave in this medium.
The frequency of a wave stays the same regardless of the material of the media. However, the speed of a wave indeed depends on the material of the medium (density of the medium, etc.)
and stays the same regardless of the medium. Thus, the wavelength of this wave in a given medium would be proportional to the speed in that medium.
For example, the speed of sound in materials with a larger density (e.g., water) is generally larger than that in materials with lower density (e.g., air.)
When a sound wave travels from air into water, the frequency of this wave would stay the same. However, since the speed of the wave would increase, the wavelength of this wave would also increase.