I have learned that due to doppler effect the wavelength of light increases when source is moving away from observer. Also this proves big bang theory and also universe is expanding. Like red shift , is there anything like blue shift that decrease the wavelength of light? Is there any experiment or evidence for this? I also heard that introduction of 4D is responsible for velocity of light to be constant in this process. Is this is true? If this is true then how the velocity of sound is constant since the velocity of sound is less?
To start with, the velocity of light is not the same for all observers. It is the speed of light that does not change when observed from different inertial reference frames. The invariance of the speed of light is what led to the 4D model. Einstein wrote his papers on (special) relativity before Minkowski (Einstein's professor) introduced the notion of 4-dimensional space-time.
Velocity is speed in a specific direction. The direction of light will, in general, change from one inertial frame to another.
One view of light propagation is that it has no medium. Air (or some other continuous material) is the material medium of sound. That medium has non-zero (rest) mass. Sound is a disturbance in that material which is communicated between adjacent elements which are otherwise at rest in some inertial frame.
Yes there is such a thing as blue shift. I can't cite a specific example, but I am certain there is some stellar jet, somewhere, whose material is moving toward Earth, and therefore exhibits a blue shift.
Also, the moving target indicator feature of the radar I worked on in the Army used the change in frequency of the reflected radiation to distinguish a moving object from stationary background reflections. If the target was approaching, the return signal was "blue shifted".
Another opinion regarding the medium of light (which I prefer) is that the medium of light is geometrodynamic space-time.