| > you cannot calculate anything. What one would formally do is represent these as points of an imaginary unit sphere centered on the observer. There is an angular distance between those two points (one located using our hearing, another located using eyesight), which is what is observed as "plane not being where you hear it". While one can't calculate much from these observations, it doesn't take much to get there: all you need is another similar observation (eg. at the time when the plane sounds as if it's where you first observed it) along with measuring the time between those measurements (say, counting seconds if you don't have a stopwatch, since we are very imprecise anyway). The time it took the airplane sound to "move" between these two points is how long it took for sound to reach you from the first observed plane position. And now you've got the distance from you (speed of sound multiplied by time) at that point. With a few assumptions which are applicable to experiments like this (eg. constant airplane velocity, and climb rate being either small or constant), you can also establish where the plane was when the original sound was emitted, what's the speed it travels at, etc. Error bars in all the measurements would be pretty huge if only observing with eyes and ears and by counting, but the fact that the effect is easily noticed even with all those "measuring errors" is fun to consider. You can also move to much better instruments to measure all of these (including direction the sound is coming from). |