Question

When a wave travel from one to another medium what is the relation between amplitude and velocity?

Answer 1

None.

For any wave, the amplitude can be anything.

There is a simple relationship between wavelength, frequency, and velocity. You can see this easily: a wave travels one wavelength L in one period P, so v = L/P. The period P is defined as the inverse of the frequency f, so P = 1/f. Put these together and you get v = Lf.