5 ms·
Like any general explanation, I think some simplification is helpful :) I may have been assuming that it was clear in the article, but to help show the effect,
by otras 4y ago
Like any general explanation, I think some simplification is helpful :)
I may have been assuming that it was clear in the article, but to help show the effect, the diagrams show only the sound emanating from the plane at one instant in time. In reality, the aircraft is continuously moving, and there's a continuously changing "where is the sound coming from" vector. The main idea is that this "where is the sound coming from vector", if you will, may be behind the plane's light vector (which we can just say is the plane's position) if you're some distance away, leading to this oddity.
> the sound may be able to reach you much much earlier than the plane
I completely agree! I didn't mean to say that a plane's sound is always behind it — it very much depends on the position of the observer. If a plane is flying in any other direction than perfectly perpendicular, the math and the effect will be different.
For "If the plane was moving very slowly, it wouldn’t outpace its sound by much.", I meant in the sense that we, as observers, are perceiving the sound. More that the plane's position vector wouldn't outpace the "where is the sound coming from vector" by as much (a smaller X in the diagram, if you will), leading to "where is the plane" being closer to "where is the plane's noise". Going faster than the speed of sound leads to all sorts of very interesting questions, but I don't believe it would affect this in the simple case we're looking at.
- bernulli 4y agoHi Otras, a few things to wrap this up for me, and thank you for your civil answer to a not so civil comment. 1st: I should have made this a 'yes and' rather than a 'no but' comment. It's a well written article with nice illustrations, and you put in the time to do so and share it with the world. Thank you for that! 2nd: Obviously you're right that it's possible to calculate the distance to plane by observing when it passes a certain point and then measuring the time until the sound hits you from that very point. 3rd: My smartassery still stands that "How far behind a plane is its noise?" is a misleading way to frame it - the noise is not behind the plane at all, it's actually significantly ahead of it. But (!), again, I should have made that a 'yes, and' instead, to add a facet to your nice article. Cheers, and hope to read from you again!
- bernulli 4y agoThanks for chiming in! My point is that your one instant in time is completely arbitrary. You do not know where the position is, and you do not know when the sound was emanated. I.e., you cannot calculate anything. Your math would work iff you observe a discrete event where you can tie sound and light - engine blow-up, for example. In all other cases, it means nothing. Again - why don't you hear the sound of the aircraft taking off if speed of sound is the only effect?
- Retric 4y agoNow is a specific instant that corresponds do a different specific instant in the past when the sound was produced by the aircraft. The same is true of any arbitrary point in time you pick. So, 5 weeks ago you may have heard the aircraft take off but that’s irrelevant to what you experience right now.
- necovek 4y agoYou've got two approximations we are used to working with. One is our eyesight, which is pretty precise (error depending on the speed of light) — of course, I am not getting into all the potential ways our eyesight can fail us. Another is our stereoscopic sound positioning based on having two ears, which is ultimately much less precise, but can still point in a general direction of where the sound you are hearing right now is coming from. If you've got both functioning ears, you can usually tell if someone is calling you from the front, either side or from the back. Some people are better at it than others, though. Sound you are hearing right now (a discreet event) has been emitted at a particular point by an airplane a number of seconds/minutes away — this is what identifies the "discreet" point and requires no remarkable event like an explosion, and you can do the math based on that and the two "instruments" you'd use. I am not sure why would it matter that airplane produces the sound continuously for discussing this discreet moment in time when a particular sound was produced? (unless you are going for there being no vibration of air possible without time passing, which is needlessly picky).
- dTal 4y agoExcellent post, however the word you likely mean is spelled "discrete" - a "discreet" event would be hard to hear :)