So why don't you hear the sound when it all begins, right at take-off? That should be the first sound to reach you, no?
I would assume you do, only it's so far away and your ears aren't powerful enough on their own to make it out. (If it can even be picked up over the other background noise.)
For another thought experiment: if you cannot hear that original first sound on take-off, which one can you hear? 10 miles from you? 1 mile from you? That will be the virtual first sound to you, determined by how much weaker the sound has become on its trip through the atmosphere, and how that relates to your hearing threshold. But it will not always and exactly be at the point where the plane has reached its closest point to you (as in the article).
I think I get what you're saying now. Thanks for taking the time!
Sorry, I thought the first answer was so short it seemed rude, which is not what I intended.
Wait, does it have to be that complicated?
A plane flying X feet above you ought to make the same noise as a plane flying X/2 feet above you, except at 1/4 of the volume, and lagging by something like twice as much (meh trigonometry was never my forte). What am I missing?