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I feel you're overcomplicating things and/or are describing some different phenomenon. The point isn't the question whether it's the sound, the light or the airplane itself that reaches you first. The question is which direction is the sound coming from.

Imagine a plane flying 3 km high, circling around your location in a circle with radius 4 km. In other words, the plane is consistently sqrt(3² + 4²) = 5 km away from you. Let's assume the speed of sound is at a constant 343 m/s in this scenario, so sound takes 5e3 m / (343 m/s) = 14.58 seconds to travel from the plane to you. The direction of the incoming sound that you detect will change all the time, at the same speed as the direction of the plane itself, but it will lag behind. The sound that you hear at each moment is the sound that the plane generated 14.58 seconds before, and you detect it as coming from the location the plane was in at that moment, and not the current time. Your eyes (or a camera, or a radar) detect the plane from one position, your ears (or a directional microphone) detect it from another, older, position.

All that is true independently from the speed of the plane, be it subsonic or supersonic (except when the plane is flying very slowly, or if it's a hovering helicopter: in those cases the sound is still delayed, but the location it's from is hardly changed or not at all).

Strictly speaking the same happens with the visual image, but since light is so much faster we can neglect the delay it causes in every-day situations like this.

Haha, yes, you found the one case (which is unrelated to the article) in which sound weakening is not a function of time, as the distance to you stays constant.

But it's not talking about the aircraft itself. The article is talking about the comparison of the visual image of the aircraft and the sound coming from the aircraft:

"You can hear the loud engines, and your ears tell you it should be in one place, but your eyes tell you it’s clearly well ahead of its noise."

What time the aircraft passes the observer is irrelevant (if you Ctrl+F for pass in the original article, it's not there) and the correct calculations for an aircraft traveling 100m/s would be:

If you're 100km away, the image of the plane will reach you after 1.20 milliseconds (100km / speed of light in air), and the sound will reach you in 333s. (in which the plane now has moved 33.3km and now you're getting an image of a plane 66.7km away.)

If you're 200km away, the image of the plane will reach you after 2.40ms and sound will reach you after 667s.

The main thing this effect relies on is the ability for an object to move a significant fraction of its size in the time it takes for the sound to reach you.

> This describes the case of a plane suddenly appearing in mid-air

False.

> and starting to make noise

False

> As long as it flies subsonically, i.e. sound outpaces the aircraft...

> If you're 100km away, the aircraft will reach you after 1000s...

These statements exhibit a fundamental misunderstanding of the phenomenon. It's not that the sound outpaces the aircraft. It's that light from the aircraft (reflected or transmitted, e.g., by landing / navigational lights) travels faster than sound.

When light from the aircraft reaches you, the sound is lagging behind the light.

At the height of a jet airliner (~FL30, 30,000 feet), light reaches you in 30 microseconds. At the height of a small plane, about 3,000 feet, say, it's 3 microseconds.

Sound takes 27 seconds to reach you from the jetliner, and 2.7 seconds to reach you from the small plane.

If the jetliner is flying at 600 mph (~mach 0.8, ~515 knot) the aircraft has travelled 4.6 miles (7.4 km) from the position from which its sound was emitted before that sound reaches you. The apparent position indiciated by vision and sound don't match.

If the small aircraft is travelling at 122 knots (140 mph) (cruise speed for a Cessna 172), it has travelled about 1/10 mi (0.16 km) before the sound reaches you. That's about 550 feet.

Both cases are for when the aircraft its directly overhead. The apparent difference will increase as the aircraft is closer to the horizon (arriving or departing).

Again, the visual position and apparent aural position of the aircraft are not the same.

You can determine this yourself, if you're outside and hear a jet aircraft flying at altitude. If you look to where the sound appears to be coming from you will not see the aircraft. It is going to be nearly 5 miles further along its path of travel. It can be surprisingly difficult to visually find the aircraft if you've only first heard it. If instead you're watching the sky and first see the aircraft, it will be quite some time, about 30 seconds, before the sound reaches you, and that sound will seem to be considerably far back along the aircraft's path of travel.

> It's that light from the aircraft travels faster than sound.

For all practical purposes we can say the light reaches the observer instantly, whereas the sound takes some (significant by comparison) amount of time. Over such short distances, and when comparing it to something that is so much slower (299,792,458 m/s vs 343 m/s, 874 thousand times faster), there is no point in measuring the infinitesimal time it takes light to travel the distance from the plane to the observer.

For the general case presented in the article, at the average cruising altitude and speed mentioned within it, the conclusion is that it takes sound from the plane so much longer to reach the observer than the instantaneous light from the plane, that the actual plane itself has traveled another 2.1km in that time. You are (instantly) seeing the current position of the plane but hearing the sound it emitted 2.1km ago.

Ok, you can adjust my illustrative example of O(100s-1000s) by the 30ms to account for a finite speed of light if you think that makes any difference to the argument. Let me know.

This has got to be a troll. I have trouble believing you are being serious saying things like this.

That we can calculate the distance to a lightning to great accuracy (my example in the very first sentence) by accounting for a finite speed of sound only and assuming an infinite speed of light? Yeah, I'm pretty serious that we can neglect that error of some microseconds when concerned with a process that takes many orders of magnitude more.

https://jkorpela.fi/wiio.html

> " These statements exhibit a fundamental misunderstanding of the phenomenon. It's not that the sound outpaces the aircraft. It's that light from the aircraft (reflected or transmitted, e.g., by landing / navigational lights) travels faster than sound."

Explain to me again how any of that explains why the airplane passes me (and I see it 1e-6s later which seems to be somehow super important to you) before I hear it, even though its sound is traveling towards me much faster than the plane.

You're demonstrating Wiio's Law.

Seems to cut either way.

Slight tweak: it's 30 microseconds, not 30 milliseconds. But I wholeheartedly agree with your points!

For all practical purposes it's really completely unrelated to the speed of light. Nothing would change in the argument if light travelled instantaneously. Sure, the numbers would change by O(1e-6s), but I'll admit that I wouldn't be able to tell the difference when watching an aircraft.

Precisely my point.

I'd meant to edit my post to note that for the purposes of this phenomenon, light speed is instantaneous.

Though in the more general case, the phenomenon would apply to any case in which two signals or channels travel at different rates or speeds. Light and sound are the examples most familiar to us, though other alternatives exist.

Neutrinos can tell us what is occurring at the core of the Sun with an ~8 minute delay whilst the propagation of EMR effects from the Sun's core is thought to take 10,000 to 170,000 years, as these travel through repeated collisions, absorption, and re-emission.

Diffusion processes such as smell or other chemical materials both travel more slowly than either light or sound, and at different rates for different compounds --- heavier compounds diffuse more rapidly than lighter ones. This is incorporated into the chemical signalling processes evolved by insects such as ants, in which some compounds are heavy and complex (usually for food or other valuable resources), others are light and fast (danger or alert signals). Again, for a moving or propagating phenomenon, these will move at different rates.

For more complex phenomena, you might note that there are early / rapidly-moving indicia and those which move more slowly. Again, understanding the difference between these, the rates at which they travel, and their association and interactions with the processes originating and surrounding them will assist in drawing an accurate inference of the root phenomenon.

All sensation is mediated, not direct, and that mediation has a direct effect upon sensation.

You're the one bringing up the finite speed of light that has zero relevance to the problem at hand.

Gah! Thanks, corrected in original.

> So, how come it sounds like the sound of the plane is behind the plane? It's got to do with sound attenuation in the atmosphere and your hearing threshold.

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?

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.

Precisely, "sound attenuation in the atmosphere and your hearing threshold".

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.

Hi 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!

Thanks 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?

> 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).

You'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).

Excellent post, however the word you likely mean is spelled "discrete" - a "discreet" event would be hard to hear :)

Indeed and LOL, thanks for the correction :D

Now 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.

The article is right

> So, how come it sounds like the sound of the plane is behind the plane? It's got to do with sound attenuation in the atmosphere and your hearing threshold.

> So, it's not at all like in the article.

On the contrary it is indeed because of what the article is getting at. It's because the sound emitted by the airplane at one position reaches you significantly later than the light the plane reflects from that position reaches you. Maybe what you're describing is that the sound emitted when the airplane took off reaches you faster than the airplane reaches you which sure, it's correct - but the light still reaches you way way faster.

> - "If the plane was moving very slowly, it wouldn’t outpace its sound by much." That's completely wrong. "very slow" aircraft are much slower than their sound, and all commercial aircraft still are slower than their sound, all of them are outpaced by their sound rather than the other way around.

Even if the s̶o̶u̶n̶d̶ plane (edit: meant plane) travelled faster than sound, you would still see the airplane passing over you before the sound emitted from the airplane when it passed over you reaches you.

Minor nitpick: - As an example, take an aircraft flying with 100 m/s

200 m/s would be a better example as the Boeing 737 (the most common commercial passenger jet) cruises at around 230 m/s

> "Even if the sound travelled faster than sound [sic] you would still see the airplane passing over you before the sound emitted from the airplane when it passed over you reaches you."

Absolutely not. It depends on the Mach number, distance, sound weakening, and your hearing threshold.

You cannot hear some crazyman running at you, screaming, until he has passed you? You cannot hear the stereo in some guy's car until after he passed you? You cannot hear a siren of police until the car has passed you? Or are what you describe special magical airplane-only physics?

> You cannot hear some crazyman running at you, screaming, until he has passed you? You cannot hear the stereo in some guy's car until after he passed you? You cannot hear a siren of police until the car has passed you?

For all of those things, you will see them pass you before you hear the sound they emitted when they were passing you. (Maybe not by enough to be noticeable, given the smaller distances involved)

Oops, I mean to write even if the plane travelled faster than sound, not sound travelled faster than sound.

Well yeah, if the plane is faster than its sound (and flying towards you), the plane will reach you earlier than the sound does. The plane does not get attenuated by flying farther, and your seeing threshold is helped by the sun or the lights the aircraft turns on at night.

Of course you hear the siren or crazy man or anything, before it passes you if the component of the velocity vector pointing to you is slower than the speed of sound.

But it still takes time for the sound to reach you. And in that time the source has continued to move. So it will be as if you are watching a video but hearing with a tape delay.

If some one was standing 1000 meters away from you, and had a sign that flashed a sequence of numbers, 1,2,3,4,… once per second, and at the same time as the number flashed, they shouted the number loud enough that you could hear it, do you think what you heard and what you saw would be in sync?

> "Of course you hear the siren or crazy man or anything, before it passes you if the component of the velocity vector pointing to you is slower than the speed of sound."

So, only in aircraft it is different? Magical aircraft physics after all?

> " If some one was standing 1000 meters away from you, and had a sign that flashed a sequence of numbers, 1,2,3,4,… once per second, and at the same time as the number flashed, they shouted the number loud enough that you could hear it, do you think what you heard and what you saw would be in sync?

Of course not.

But to humor you: which is the distinct event in a normally flying aircraft in which you can tie the exact point at which the light and sound signal leave the aircraft towards you so you can use that to calculate the distance? Spoiler: there isn't, you cannot, and that is precisely the point.

There are some examples currently in Ukraine, in which you could use your argument.

Well, in many planes it would be the firing of a cylinder. But you don’t need a distinct event. You look at an instant in time. It’s a fundamental of calculus called an infinitesimal.

Did you read the entire article? I think where you’re getting mixed up is that the article is using some poor assumptions and a broken thought experiment to derive a scheme for calculating or estimating the distance based on the sound/light mismatch. I don’t think anyone is claiming sound and light don’t travel at different speeds but the explanation in the article is pretty misguided.

I may have missed something, but what I saw I thought was accurate.

Is it in dispute that it takes time for the sound to reach you?

Is it in dispute that you can discern the direction from which a sound came?

Is it in dispute that the aircraft has moved during the time it takes for the sound to reach you?

Is in dispute that the sound emitted in the instant of time the aircraft is in position A will not reach you until the aircraft is in position A+k?

Is it in dispute that there are realistic velocity vectors for which the direction of sound from position A is perceivably distinct from the visually observed position A+k?

What if you imagine instead a boat traveling parallel to the shore on which you stand. Has the boat moved perceptibly from position A by the time the wavefront of the wake generated at position a reaches you?

How about this visual simulation of a moving sound source? https://www.youtube.com/watch?v=StXXPkCMREU

Or how about this video https://www.youtube.com/watch?v=6g6uJTsJ9CE

Do you notice the sound waves are not concentric?

Thank you.

The article is correct, their explanation is poor. When you hear a sound with your eyes closed you can normally locate where it’s coming from. As in close your eyes and snap your fingers. Now suppose someone sets off a bomb some distance from you. You see the explosion or lightning flash etc but it takes a while for sound to show up. For stationary objects it doesn’t really matter you can still locate direction just fine.

Aircraft in level flight are also loud enough to be heard at distance sufficient to notice a delay. If the aircraft is flying by you hear sound from exactly one instant, but it like the explosion it was produced in the past. So if you close your eyes and try to locate the aircraft by sound you will point to wherever it was when it produced that sound not where it is right now.

The same is true of every sound you hear, but normally distances are short enough and speed are low enough it just doesn’t matter.

It's just completely unrelated to why the aircraft passes you before you hear it.

They never suggested the first time you would hear it was the aircraft was already past you.

However, the maximum difference in angle between it’s current location and the location the sound comes from is just after it flew past you.

The title is "How far behind a plane is its noise?" It's not. It's ahead of the aircraft.

The noise is always pointing behind the aircraft or any moving object due to lag.

Light also encodes the direction to an objects past location, even though light is always moving faster than the object.

> The noise is always pointing behind the aircraft or any moving object due to lag.

I don't know what a pointing noise is.

> Light also encodes the direction to an objects past location, even though light is always moving faster than the object.

Yet the light is never outrun by the object, much like the subsonic plane never outruns its noise. However, here, the (fast) noise arrives after the (slow) plane. In your analogy, that would correspond to the (slow) object arriving before the (fast) light.

The direction of propagation is the way sound and light point to something. It’s why people listen to music in stereo rather than mono which sounds weird and also why telescopes work. Again simplified, but when you hear a sound with your right ear before the left that tells you something.

> arrives after the (slow) plane

That has nothing to do with the article, just your misunderstanding of what was described. At every instant in time the sound you hear corresponds to something produced by the aircraft at a specific moment in the past. Thus when someone is listing right now they hear a specific sound not the aircraft taking off.

Light from an aircraft also takes time to arrive. It might not seem relevant because of the speeds and distances involved, but the exact same thing is happening and it is relevant for light in other contexts.

Ignore the idea that the plane and it's sound are in different locations ... The key to understanding this phenomena is that there seems to be a greater discrepancy the further YOU are from the plane. Ignore the planes sound and consider the case where someone on the plane set off a firecracker. When you hear the sound from the firecracker,the plane will have moved away from that point!

Isn't that only correct if the plain is heading towards you?

The article states that the sound of the plane is not were you hear it. At least this is true

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.

Suppose observer just woke up / heard plane that is passing overhead.

Very reasonable assumption, as the plane might have taken off thousands of miles away, and will land thousands of miles away in the other direction.

In this case, no point talking about takeoff sound, as it is not detectable already at these distances.

Humans can detect reasonably well which direction the sound comes from. This direction will not match the direction they observe the airplane at.

The article is describing the mismatch between plane real position and the plane position we would detect if we were just listening to it.

> you'll have to start them where it all starts, i.e. at take-off

If we are nitpicking about minor details: the sound of a powered airplane doesn’t start at take-off but at engine start, often minutes before take-off.

Unfortunately, this is very wrong! Why does it have to be a sudden sound? The effect the article describes is the same as eg thunder, except an aircraft is continuously moving and emitting sound. The aircraft in the article is not heading directly towards the observer. It simply takes time for the sound produced at a given moment to reach the observer, but the light from the aircraft travels much faster, which is why the lag is observed. It is not ‘sound attenuation’ or ‘hearing threshold’.

> "Why does it have to be a sudden sound? The effect the article describes is the same as eg thunder"

Well yeah, that's a sudden sound. My point precisely.

So why don't you hear from your observation point the airplane (or all airplanes for that matter) as it takes off, which is when it makes its first noise? And by all means, account for a few ms of light movement if that makes you happy.

> Well yeah, that's a sudden sound. My point precisely.

But you are saying that isn’t like an aircraft - why?

> So why don't you hear from your observation point the airplane (or all airplanes for that matter) as it takes off, which is when it makes its first noise? And by all means, account for a few ms of light movement if that makes you happy.

That is attenuation! The aircraft is far enough away that all the energy from the sound is absorbed by the air and objects between observer and aircraft. Attenuation does not affect the speed the sound travels. But when the aircraft is closer to you, the attenuation is lower so you can hear the sound.

Because an aircraft does not make a sudden noise? At least where I'm from aircraft don't sound like discrete booms. I'm not sure I understand your question.

> But when the aircraft is closer to you, the attenuation is lower so you can hear the sound.

So we agree after all.

> But you are saying that isn’t like an aircraft - why?

Because last I checked airplanes in cruise flight have a pretty constant engine noise, that’s why.