Use the construction the author is using, i.e. the emanating sound waves, but you'll have to start them where it all starts, i.e. at take-off, and not simply appearing right next to you. Then, correct the drawing by having the plane move slower than the sound waves. The first sound you should be hearing as observer will be the take-off (if you could hear it) at the airport, and the aircraft will be wherever it is afterwards.