Question about Ernst Mach

[Johnny5]

I have a question about Mach's theory of sound. I am not sure how much it influenced Albert Einstein.

 

Mach did an analysis of some kind, and figured out that if you could ever reach the speed of sound in air, that there would be some kind of cone thing going on.

 

From what I briefly read, the Mach equations used v/c, where v was the speed of the object in the medium, and c was the speed of sound in the medium.

 

Einstein was a Mach fan... the v/c term, I think what Einstein did was basically apply the Mach equations to the speed of light. Einstein knew that light was a wave from Maxwell's EM theory, and for einstein the vacuum was a fluid to light, just like air is a fluid for waves.

 

So I guess I have a few questions.

 

1. Who here has seen a derivation of these Mach equations?

2. What are the Mach equations?

3. What do the Mach equations predict will happen if we ever construct a plane which can reach the speed of sound? In other words, what do they predict happens when v/c=1?

4. What is the cone phenomenon which Mach figured out?

5. Do Einstein's thoughts about the speed of light in vacuum, mimic Mach's thoughts about reaching the speed of sound waves in air?