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) The speed of light in vacuum is a universal constant independent of all the factors listed and anything else. In particular, note the surprising fact that it is independent of the relative motion between the source and the observer. This fact is a basic axiom of Einstein’s special theory of relativity.
(b) Dependence of the speed of light in a medium:
(i) does not depend on the nature of the source (wave speed is determined by the properties of the medium of propagation. This is also true for other waves, e.g., sound waves, water waves, etc.).
(ii) independent of the direction of propagation for isotropic media.
(iii) independent of the motion of the source relative to the medium but depends on the motion of the observer relative to the medium.
(iv) depends on wavelength.
(v) independent of intensity. [For high intensity beams, however, the situation is more complicated and need not concern us here.]