Frequency is a function of the energy level of the photon.

Changing the medium does not change that energy level.

medium

Velocity increases when sound waves travel from gas medium to solid medium.

As velocity = frequency * wave length and the frequency does not change, v is directly proportional to the wave length...

Hence the wavelength increases.

There's no relationship between the frequency and the medium.

The frequency of a wave is determined by the source. Once the wave leaves

the source and sets out on its journey, the frequency doesn't change, regardless

of what kind of stuff the wave encounters and has to travel through.

group velocity depends upon the frequency of the wave. such type of materials called dispersive medium.