Pardon me if I substitute a different illustration — a car travelling in a straight line, such that it passes near to you. We are all familiar with the way the sound drops in pitch as it goes past. [In the case of your speaker illustration, the difference is that the sound would be of a high pitch as it approaches, and then it would suddenly drop to the actual pitch of the sound, when the speaker stopped moving.]
This is because, for each unitary sound wave, the point at which it is generated is moving… which makes each of {the resultant sound waves that travel through the air} shorter or longer — which equals higher or lower pitch (respectively). [This is “the Doppler Effect”.]
The other part of the picture is that Mach 1 is exactly the speed at which the size of the above phenomenon reaches 0. The idea is that, so to speak, it is the speed at which the sound source moves forward so fast that the peak of the next sound wave is generated at the point that the previous one moved to (at the speed of sound). Informally, the result of this is tremendous pressure in the air at the front of the moving object.
This brings us to part 2 of your question.
In the case of an object (an aircraft, or theoretically a car or a speaker) moving towards you at {approaching the speed of sound}, any sound it makes would conceptually be of an incredibly high pitch, and would arrive at about the same time as the object… and I imagine that the actual effect would be just one big push of air, like one drum beat — a sonic boom, I guess — as much at 0.98x as at 1x.
That is… this holds even if we imagine out the effect of the object itself physically pushing the air — which is also one big push. The combined effect, practically in the real world, is just one big powerful push of air.
The immediate answer to — particularly — the title of your question is that that is a sonic boom — it happens at the speed of sound, because the source is travelling at the speed of sound. Conversely, that does not address the intent and detail of the question.
The other aspect of all this is where you are standing. In the case of a car travelling nearby (assuming that it does not actually drive over you)… there is a point at which it is travelling perpendicularly to you; at that point, the sound is of the actual pitch of how it would sound stationary.
In the case of an aircraft that travels nearby, really really fast, the same is true, but the pitch of the sounds it makes would change from extremely high to extremely low in a very short period of time. If it is farther away, the change will be slower.
Thus… the sonic boom at Mach 1 does not exist in front of the aircraft (as in, say, 100m in front)… and you hear it from the side as a big boom as the aircraft passes by… and behind the aircraft all there is is turbulent air and low-frequency sound.
So what about this pressure boom at (say) Mach 2, then? Certainly there is still all that pressurised air happening!? Again, there is no sound in front of the aircraft, and behind it all there is is turbulent air and low-frequency sound. Why is there no sonic boom as it passes? At face value, it seems to me that there certainly should be a big boom… but the real-world fact is that there is not (I believe).
I am thinking that it is like the fact that air pressure reduces to the average combined effect of all the individual air molecules hitting a surface. In the same way, the speed of sound supervenes on individual air molecules moving around [at well above Mach 1, I think] and hitting each other, but it is “actually” a pressure wave passing through air — at the speed of sound — Mach 1.
A jet at Mach 2 will certainly disturb a lot of air, but the sonic boom at Mach 1 arises from the speed of the pressure wave, not of the individual air molecules. Either way, a lot of air is disturbed — arguably twice as much at Mach 2 — but it is only when the aircraft is moving at the same speed as the pressure wave that this pressure wave-related phenomenon is generated.
As for part 1 — the volume (loudness) of the sound… . The equation about less sound at less distance is just about distance; it does not deal with sound waves getting compressed or expanded because of the source moving. Given that sound waves reduce to air pushing and then retreating (as opposed to air molecules travelling long distances at the speed of sound)… it seems to me to be an obvious and direct fact that there is more energy in the same size of push happening more times per second… but conversely that the overall average air pressure does not change.
This is a frame-of-reference problem, I’ll wager. Yes, there is more energy in the same sound pitch-compressed by an object moving towards one… but no, the ear should hear the same volume [loudness] for the same size of wave. (That is what volume is — the size of the wave.)
