Let us list some of the factors, which could possibly infuence the speed of wave propagation.
(i) Nature of the source (ii) Direction of propagation
(iii) Motion of the source and /or observer (iv) Wavelength
v. Intensity of the wave.
On which of these factors, if any, does
a. the speed of light in vacuum.
b. the speed of light in a medium (say, glass or water), depend?

Explanation

a. It is a fundamental constant. Independent of relative motion of source and observer.
b. Does not depend on the nature of te soure, directionof propagation (in the case of homogeneous isotropic medium) , motion of the source and intensity (except for very high frequencies). It is seen that velocity depends on wavelength and the nature of the medium.