Is the speed of sound influenced by the speed of the emitter? If a vehicle emits a sound , does this travel at the same speed if the vehicle is stationary or travelling at a certain speed? Does the speed of sound depend only on the properties of the medium?
Do we have to sum up the speed of the emitter to  the speed of sound in air, or not? I should say that the speed of sound does not change , because if it did there would be no sonic boom.
In that case I wonder why the fact that the speed of light is not influenced by the speed of the emitter was such a big surprise
 A: You are correct: the speed of sound does not depend on speed of emitter. Sound is a waves in the air/water/metal/etc. Waves propagating through the matter do not "remember" how they were produced, their speed depend on the properties of the matter they are going through.
It's kind of obvious for sound waves, so why similar fact was such a big surprise for light?
Because in case of sound we the speed is constant related to the medium, but in case of light there is no medium! If you are moving through the air with some speed you would see that speed of sound waves is different in your frame of reference. But this is no so for light! You emit a photon, it runs away from you with a speed $c$. Now you start to chase it with a speed $c/2$. It turns out that the photon still runs away from you with a speed $c$. This is very different from what happens when you case sound waves.
One of the first ideas when people found the speed of light is constant $c$ was that there is some medium (ether) so that the speed of light is $c$ relative to this medium only. But it turned out to be a false hypothesis. There is no some special medium or special frame of reference where speed of light is constant. It turned out that speed of light is constant in any frame of reference (well, any inertial frame of reference - that is the frame of reference which moves with constant speed). If you think it's impossible than you probably understand why this was such a big surprise for physisists.
A: Speed of sound will always be same with respect to the medium ,afterall sound is just vibration of molecules in air and its speed depends on how the molecules vibrate,not on who is making the vibrations.
Speed of sound in air relative to the medium is 330m/s ,no matter who is making the sound.
Ofcourse if you are moving relative to the medium on a vehical ,speed of sound will be different for you than 330 m/s as velocity addition formula says.
In case of light no matter who is observing, the  speed of light is always the  same .The speed relative to ground ,the speed relative to the vehical ,speed relative to me,speed relative to you are all the same.That is the big surprise.
A: Please refer to Doppler' Effect. Here is the link :
https://en.m.wikipedia.org/wiki/Doppler_effect
