What causes a sonic boom when traveling at Mach 1+?

[QuantumCrash]

Here's a problem that's been bugging me.
We know that we get sonic booms because of the Doppler effect since, for an example, the jetplane over takes the soundwaves that it emits some time ago because it is travels faster than the speed of sound.
The overlapping of new sound waves it produce will cause the sonic boom.
(Feel free to correct the physics, I'm new at this topic)

Let us suppose that we are an insubstantial observer following behind the jetplane at exactly the same speed. What would we actually hear when the plane breaches the sound barrier?

 

[LURCH]

We shouldn't hear anything denoting the crossing of the sound barrier. The "sonic boom" travels outward form the leading edge of the object making it. This forms a cone of sound that we the observers would be inside of (->). Never coming into contact with the "edges" of the cone, we would never hear the sound.

I'm assuming you named us an "insubstantial observer" so that we are making our own sonic boom, right? So, if wew are close enough and listening hard enough, we'd be hearing the rattling of the jet's bits & pieces due to increased turbulence as it approached mach1. Then we'd hear that all stop when it passed throught the sound barrier and the ride smoothed out once again. But we wouldn't hear the boom.

 

[QuantumCrash]

Actually, I wrote "insubstantial observer" to avoid any complications such as being subjected to intense heat from afterburn or being affected by air resistance. What I meant was that we are, say 50m directly behind the jet traveling at the same speed.

I posted this since the normal sonic boom models that we see are assuming that we are stationary. But what would we hear if we were following the source of the boom?

 

[LURCH]

Ah, I get you. Anyway, we would not hear the boom. Actually, this hypothetical situation would put us in exactly the same position as the pilot of the jet. The nose of the jet is what makes the sonic boom, and the pilot sitting several feet behind the nose doesn't hear it. Make the jet 50m long, and you could sit at the tail end and make direct observations. So I suppose your thought-experiment has been done in real-life by anyone who sat in the rear-most seats fo the Concord! (they heard no boom)

 

[QuantumCrash]

That sounds logical I suppose. However, I always assumed that the engine was the source of the sonic boom since it was the one making the the noise in the first place. Effectively, this would result in exactly the same effect, but it would differentiate my thought experiment and those seated in the concorde since they are sitting in front of the noise source.