Postulate of constancy of speed of light in vacuum I'm not of course questioning the constancy of the speed of light, just the way the postulate about it is worded. It is often stated that the speed of light is independent of the motion of the source. Einstein himself said "and also introduce another postulate, which is only apparently irreconcilable with the former, namely, that light is always propagated in empty space with a definite speed $c$ which is independent of the state of motion of the emitting body."
But even in classical physics, isn't the speed of a wave independent of the motion of the source? Once the wave is emitted, its speed just depends on the medium. If I have a loudspeaker moving toward me, the frequency of the sound will be higher but not its speed. If I am moving toward the loudspeaker, both the frequency and the speed of the sound will be higher.
This postulate of relativity is sometimes stated in terms of the state of motion of the observer, but it is frequently stated just in terms of the source, which is what I am questioning.
 A: There is no medium.  The equations stand alone.  The possibility that empty space may itself be a stationary medium for somebody has been disproved by experiment.
Hence, any electromagnetic propagation in empty space always seems to any inertial observer to proceed at the universal constant speed irrespective of where it has come from or where else it might be going.
But for the observer measuring it, his observations depend on the source, not on other observers.  The postulate says how it depends on the source.
And of course, counter-intuitively, says it doesn't.
A: The doppler effect in classical physics works just as well if you are moving towards or away from the source or if the source is moving towards or away from you. Relative motion is what matters. 
A: "I want to emphasize that light comes in this form - particles. It is very important to know that light behaves like particles, especially for those of you who have gone to school, where you probably learned something about light behaving like waves. I'm telling you the way it does behave - like particles. You might say that it's just the photomultiplier that detects light as particles, but no, every instrument that has been designed to be sensitive enough to detect weak light has always ended up discovering the same thing: light is made of particles." Richard Feynman, QED: The Strange Theory of Light and Matter p. 15  https://www.amazon.com/QED-Strange-Theory-Light-Matter/dp/0691024170
"Moreover, if light consists of particles, as Einstein had suggested in his paper submitted just thirteen weeks before this one, the second principle seems absurd: A stone thrown from a speeding train can do far more damage than one thrown from a train at rest; the speed of the particle is not independent of the motion of the object emitting it. And if we take light to consist of particles and assume that these particles obey Newton's laws, they will conform to Newtonian relativity and thus automatically account for the null result of the Michelson-Morley experiment without recourse to contracting lengths, local time, or Lorentz transformations. Yet, as we have seen, Einstein resisted the temptation to account for the null result in terms of particles of light and simple, familiar Newtonian ideas, and introduced as his second postulate something that was more or less obvious when thought of in terms of waves in an ether." Banesh Hoffmann, Relativity and Its Roots, p.92  https://www.amazon.com/Relativity-Its-Roots-Banesh-Hoffmann/dp/0486406768
"Emission theory, also called emitter theory or ballistic theory of light, was a competing theory for the special theory of relativity, explaining the results of the Michelson–Morley experiment of 1887. [...] The name most often associated with emission theory is Isaac Newton. In his corpuscular theory Newton visualized light "corpuscles" being thrown off from hot bodies at a nominal speed of c with respect to the emitting object, and obeying the usual laws of Newtonian mechanics, and we then expect light to be moving towards us with a speed that is offset by the speed of the distant emitter (c ± v)."  https://en.wikipedia.org/wiki/Emission_theory
