Can we hear a supersonic plane?

[andrewkirk]

A very clever first-year physics student I know, who had just been learning about the Doppler effect, asked me a question. If a plane were flying a straight trajectory at Mach 2, playing a song on its speakers very loudly, and an observer with incredibly sensitive recording equipment were to position themselves in the wake of the plane just after it had passed, would they hear the song playing backwards?

There are a number of interesting aspects to this question. One that I found myself puzzling over was whether one could hear any sound at all from the plane itself, other than the sonic boom as it passed. I am not interested in questions of relative loudness, such as that the roar of the engines would drown out the song. One imagines that, with the right equipment, one might be able to separate the two waveforms and detect that of the song - at least in theory, if not in practice.

What I was wondering was whether the sonic boom phenomena around the plane actually prevents one from detecting any sound wave emitted by the plane itself. What made me think that was that behind the plane there will be a near vacuum, preventing the transmission of sound backwards. In front of the plane is the very high pressure front of the sonic boom, and any wave that would otherwise be transmitted forwards is immediately destroyed by the plane crashing into it. Maybe sound can only escape in directions that are close to perpendicular to the plane's direction of travel - away from the rear vacuum and out of the way of getting smashed by the plane. But in that case one would only detect the sound very briefly as the plane passed directly overhead (again ignoring issues of volume).

My initial reaction was that of course that is wrong because a ground observer hears the sonic boom and then hears a lower, continuous roar. But I thought that what we might be hearing there is not the engines themselves, which are shielded from us by the vacuum/boom-front, but the noise of the jet stream that is fired backwards by the engines, as it hits the air behind the vacuum. Because that collision occurs outside of the sonically shielded region immediately around the plane, it is free to propagate and so we can hear it.

Anyway, my question is this:

Could sound produced by a plane - such as if it had a very loud police siren blaring - be heard away from the plane with suitably sensitive equipment if the plane were traveling supersonically?

 

[Bystander]

Does the air move? Yes.
Or stand still? No.

 

[rootone]

I don't think so.
Every noise made directly by plane will be heard compressed as the 'boom', a shock wave, by observers on the ground shortly after the plane passes overhead.
(actually I think it sounds more like snap-crack than boom. although I only personally heard a sonic boom on two occasions)
That might be followed by a series of indirect echos of the boom from buildings or high terrain in the area.

 

[andrewkirk]

Does the air move? Yes.
Or stand still? No.

Can you elaborate? It is unclear how these questions and answers relate to my question.

 

[Bystander]

An ideal (still) vs. a non-ideal (moving) medium.

 

[boneh3ad]

You can still hear supersonic planes, and if you are directly behind it you actually won't hear a boom anyway since a sonic boom comes from the oblique shocks coming off the various parts of the plane (notably the nose and tail).

There is no vacuum that prevents sound from traveling behind a supersonic plane, either. As a sound wave is emitted, it will travel out roughly spherically from the point it was created in all directions at the local speed of sound, including backward.

Randall Munro sums it up more amusingly than I can: https://what-if.xkcd.com/37/

 

[russ_watters]

And what does it sound like? Playing back? No. Just very doppler shifted.

 

[andrewkirk]

And what does it sound like? Playing back? No. Just very doppler shifted.

I don't think so. I suspect you are thinking of the Doppler shift for EM waves. The shift for sound is different in a number of important ways.

 

[Nidum]

For anyone that has never heard a sonic boom :

 

[andrewkirk]

@boneh3ad Awesome link! It's uncanny. I had originally drafted in the OP a quip about the song being Stairway to Heaven and that you would hear it telling you to worship Satan after the plane passed, but I took it out because I thought people might not take my question seriously.

And then in your link, that delightful graphic, with the person hearing 'Worship Satan'.

The link also covered something else I had figured out, which is that you would hear both forwards music and backwards music simultaneously.

I haven't worked out yet why it says the backwards music would be rising in pitch. I thought it would be at a constant interval above the original pitch. I'll need to do some more calcs.

 

[russ_watters]

I don't think so. I suspect you are thinking of the Doppler shift for EM waves. The shift for sound is different in a number of important ways.

Please explain what you mean in more detail: what do you think you will hear and why? What is wrong with my explanation?

There is no vacuum behind a supersonic plane. The plane makes noise, so the air carries away the sound.

 

[andrewkirk]

Please explain what you mean in more detail: what do you think you will hear and why?

See link in post 6. Although I wasn't aware of that linked web page when I started the thread, it presents a good summary of why - to the extent that one could discern anything of the music - one would hear it backwards as well as forwards. Anything I wrote would just overlap it.

 

[boneh3ad]

Please explain what you mean in more detail: what do you think you will hear and why? What is wrong with my explanation?

For one, it is possible to travel faster than the speed of sound but not the speed of light. Given that this is a question about a supersonic sound source, it doesn't have an EM equivilant since superluminal travel is not thought to be possible.

 

[nsaspook]

If you listen closely you can hear the jet thrust pitch change as it moves overhead after the shock wave. It would take one really loud boom box to be heard over that.

 

[russ_watters]

For one, it is possible to travel faster than the speed of sound but not the speed of light. Given that this is a question about a supersonic sound source, it doesn't have an EM equivilant since superluminal travel is not thought to be possible.

That's fine, but I don't see what it has to do with my post.

 

[russ_watters]

See link in post 6. Although I wasn't aware of that linked web page when I started the thread, it presents a good summary of why - to the extent that one could discern anything of the music - one would hear it backwards as well as forwards. Anything I wrote would just overlap it.

Fair enough. I did miss that it can go backwards for a short time. But you mentioned Doppler shift as being an error in my post. The link mentions Doppler shift, though not by name. Just to make sure it is clear, there are several things happening and also some parts of the link that are misleading:

1. Sound waves don't quite propagate in all directions from an object moving faster than the speed of sound, as implied by the diagram with the circles. The front quadrant (roughly) is cut off by the shock wave (they are part of the shock wave) and the airplane (to propagate forward with respect to the ground and backwards with respect to the plane, they would have to propagate through the plane). At mach 2, by a 30 degree wedge, that's 90 degrees cutoff.

2. Because of #1, the "forward" propagation of the sound waves is limited by the mach cone. That means that the amount of backwards playback is similarly limited. By my calculation with some simple geometry and arbitrary altitude of 11,000 feet, you get 4 seconds of backwards and forwards sounds mixed together. After that, for as long as you can still detect it, you only get forwards sounds, doppler shifted.

3. The link says after that, the sound would be heard progressing forward at half speed and an octave lower. That's not quite true: just like with a moving train or ambulance siren, the sound frequency changes as the angle between the object and observer changes. But it will eventually settle on that maximum doppler shift.

 

[JBA]

The Concord video is interesting but due to its altitude doesn't have the same sensory impact as that demonstrated in one of the US Air Force air shows that I attended many years ago during which, while everyone is focused on the activities above the airfield, you see a fighter flying over Mach 1 pass directly overhead from behind totally silent until shortly after it passes its sonic cone (boom) hits you.

 

[mfb]

For one, it is possible to travel faster than the speed of sound but not the speed of light. Given that this is a question about a supersonic sound source, it doesn't have an EM equivilant since superluminal travel is not thought to be possible.

You cannot beat the speed of light in vacuum, but you can be faster than the speed of light in a medium, where you get the same effects as we get with the supersonic jet. Plus Cherenkov radiation.

Sound backwards and forwards.

2. Because of #1, the "forward" propagation of the sound waves is limited by the mach cone. That means that the amount of backwards playback is similarly limited. By my calculation with some simple geometry and arbitrary altitude of 11,000 feet, you get 4 seconds of backwards and forwards sounds mixed together. After that, for as long as you can still detect it, you only get forwards sounds, doppler shifted.

There is no limit on the time you get backwards sounds. The sounds played 1 minute before you hear the airplane have been played at a distance of about 2 "sound-minutes", so you'll hear them two minutes after the airplane passes you. Well, in theory, because hearing sound over ~40 km distance is impractical.

 

[CalcNerd]

My opinion only: As the plane passes overhead, you will hear two sonic booms, one from the nose and the other from the tail. Usually, the plane is to short to actually distinguish these two booms. On a larger Concord or B-1 bomber, you could probably be able to hear these two booms. The second boom emanating from the tail of the plane destroys all sound information that could possibly be heard from the plane.

 

[mfb]

Sound waves are linear to a good approximation, there is no destruction going on.

You could indeed hear two separate booms from the Concorde. From Falcon 9 you can even hear three (engines, landing legs as they start to deploy, grid fins).

 

[CalcNerd]

Sound waves are linear to a good approximation, there is no destruction going on.

You could indeed hear two separate booms from the Concorde. From Falcon 9 you can even hear three (engines, landing legs as they start to deploy, grid fins).

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You agree there are two or even more separate booms, yet state no destruction is going on. How would you recover a linear sound function of say 50 dB inside the cabin when your boom is 140 dB at the tail? Is there any theoretical basis for this logic?

 

[mfb]

You agree there are two or even more separate booms, yet state no destruction is going on.

Two separate booms are just an example of sounds from different sources adding without nonlinear effects.

Where exactly do you expect nonlinear effects, and why?

 

[CalcNerd]

Two separate booms are just an example of sounds from different sources adding without nonlinear effects.

Where exactly do you expect nonlinear effects, and why?

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I believe the original poster had the following question.
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What I was wondering was whether the sonic boom phenomena around the plane actually prevents one from detecting any sound wave emitted by the plane itself. What made me think that was that behind the plane there will be a near vacuum, preventing the transmission of sound backwards. In front of the plane is the very high pressure front of the sonic boom, and any wave that would otherwise be transmitted forwards is immediately destroyed by the plane crashing into it. Maybe sound can only escape in directions that are close to perpendicular to the plane's direction of travel - away from the rear vacuum and out of the way of getting smashed by the plane. But in that case one would only detect the sound very briefly as the plane passed directly overhead (again ignoring issues of volume).

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As the tail of the plane has another Boom following it, all sound between the tail and point of the aircraft have to reside between the two booms. How do you recover that information (even theoretically.)? You seem to imply that you can as you believe this cabin signal isn't destroyed by the tail boom.

 

[mfb]

all sound between the tail and point of the aircraft have to reside between the two booms

You claimed that twice now, without any argument why. And it is clearly wrong, as you can hear supersonic aircraft after their sonic boom(s).

How do you recover that information (even theoretically.)? You seem to imply that you can as you believe this cabin signal isn't destroyed by the tail boom.

How would such a destruction look like?

 

[CalcNerd]

You claimed that twice now, without any argument why. And it is clearly wrong, as you can hear supersonic aircraft after their sonic boom(s).How would such a destruction look like?

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Because it's obvious. If you and I are discussing this on the Concord (legacy flight??) or perhaps we're getting a lift on a B-1, our conversation takes place inside the plane (between the two sonic booms).
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So that conversation is physically sandwiched between the two physical booms the aircraft (sound is a physical phenomena, not like EM waves). The boom is so much more violent (to the air molecules) that no intelligible signal can be recovered. The tail end boom effectively destroys this information. However, if you believe there is a method to recover such a conversation, I would like to know what your methods would be (even a theoretical solution).
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As to your hearing the plane after its sonic boom, are you sure you are actually hearing the plane or simply the echo of the sound from the sonic boom as it rolls away from you?

 

[mfb]

Because it's obvious.

How can something be obvious if it is disputed?

If you and I are discussing this on the Concord (legacy flight??) or perhaps we're getting a lift on a B-1, our conversation takes place inside the plane (between the two sonic booms).

I don't see the relevance of the perspective of passengers on board.

So that conversation is physically sandwiched between the two physical booms the aircraft

That does not make sense.

(sound is a physical phenomena, not like EM waves)

That makes even less sense. You think light (for example) is not a physical phenomenon?

The boom is so much more violent (to the air molecules) that no intelligible signal can be recovered.

We were ignoring practical considerations here all the time. The sonic boom is a short-term event, we can listen before and afterwards.

 

[jack action]

OK, I'm chiming in. Maybe I don't understand what some are saying - and I'll repeat the same thing - or I don't understand sound waves.

First, there are pressure waves and sound waves. Although similar (they both travel at the same speed, i.e. speed of sound), they are two very different things.

Pressure waves

Pressure waves are much much stronger than sound wave and they are an aerodynamic phenomena, i.e. an object moving into a fluid. As soon as there is a pressure variation, there is a pressure wave sent at the speed of sound to «inform» the fluid ahead that a pressure change is coming. The pressure variation is determined mostly by the object' shape.

When the object goes faster than Mach 1, then the pressure waves sent in front of the object «pile up» creating a shock wave, releasing an enormous amount of energy, leading to a sonic boom. Similarly, a negative pressure wave (think vacuum) is sent behind the object which leads to a second «pile up», thus a second sonic boom. Note that it is possible to design an object that do not produce those [external] shock waves and sonic booms (Busemann's Biplane). Also, there are 2 major sonic booms with an airplane, but there are others - weaker - for all protuberances of the airplanes:

(source)​

Sound waves

When you consider sound waves only, for an object going faster than Mach 1, the same thing should happen, but with far less energy release. In front of the Mach cone, no sound can be heard. Why? Because all the sound waves emitted are «piling up», which should create a «mini» sonic boom (again, sound waves are orders of magnitude below pressure waves). So you will never hear music playing backward, except maybe in the thickness of the shock waves (I don't know about sound waves, but with pressure waves, the thickness of a shock wave is about 200 nm).

Behind the shock wave, you will only have the «rear» portion of the sound waves emitted, so the sound waves will be in the correct order (no «backward playing») with a phase shift leading to a lower frequency (like a moving car siren).

Summing it up (not taking pressure waves into account):

1. I see the supersonic music box coming towards me and hear nothing;
2. As it passes by, I hear a mini sonic boom;
3. As I look at the supersonic music box going away, I hear the music playing in a lower frequency.

Does that make sense or am I missing something?

 

[CalcNerd]

It seems I am not being clear enough for you, it is probably beyond my ability to make this argument more clear.
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We were ignoring practical considerations here all the time. The sonic boom is a short-term event, we can listen before and afterwards.

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Sorry that I am going to return to the original point and not address all of the aspects in between. How are you going to listen to the plane that is moving away from you at 2 times the speed of sound and is shielded by a sonic boom from the tail of the plane? While you claim that you hear the plane as it recedes in the distance, are you sure? Can you provide some proof that you are actually hearing the plane and not sound reflection from other sources.
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mfb: With your logic, you can certainly confirm Jack Actions results, where as I would say his music is completely obliterated by the rear projection of the boxes second supersonic wave.

 

[jack action]

where as I would say his music is completely obliterated by the rear projection of the boxes second supersonic wave.

I'm not saying you are wrong, but are we sure about that?

Pressure waves don't destroy themselves because they cross each other, but I'm not sure about crossing shock wave. Especially that the rear shock wave would be negative and the sound wave would be positive.

For the front shock wave it is not the same thing: It is not that the sound waves are destroyed by the shock wave due to the accumulation of pressure waves, it is just that they can't go fast enough to pass them, thus the accumulation.

 

[mfb]

How are you going to listen to the plane that is moving away from you at 2 times the speed of sound and is shielded by a sonic boom from the tail of the plane?

It is not shielded, in the same way gravity still acts on objects blown away from a nuclear explosion nearby. It is just harder to measure.

While you claim that you hear the plane as it recedes in the distance, are you sure? Can you provide some proof that you are actually hearing the plane and not sound reflection from other sources.

Sure, do a frequency analysis.

 

[rcgldr]

On a bit of a side note, the boom you typically hear from a supersonic jet at a relatively large distance is a normal sound wave that the shock wave degrades into as it's amplitude diminishes over distance and time. An actual shock wave sounds more like a crack, as heard in this video:

 

[Ketch22]

This is in actuality a fascinating discussion. I do have an additional bit of input to throw in that I will not attempt to calculate as it might make my brain hurt.

I know and often demonstrate for classes that it is possible to cancel all sound when the two waves are 180^oout of phase. Of course with low frequencies this is easy to accomplish perfectly with little effort. As frequency of the sound increases it is easier to approximate due to reduced wave length but less effective as the interaction is more limited.
To actually calculate this with a broad spectrum sound on the compression side of two different doppler shifted waves, well one would have to pitch in for a lot of my time to see how it goes.

 

[andrewkirk]

all sound between the tail and point of the aircraft have to reside between the two booms

it is clearly wrong, as you can hear supersonic aircraft after their sonic boom(s).

I am very much enjoying sitting back and just learning from the discussion. But while not yet understanding what happens to sound emitted from the body of the plane, and the extent to which its propagation is constrained, I do have a theory - which I advanced in the OP - as to why we can still hear a supersonic plane after the boom passes, even if the two booms did somehow prevent the propagation of sound from the plane body. Here it is:

My initial reaction was that of course that is wrong because a ground observer hears the sonic boom and then hears a lower, continuous roar. But I thought that what we might be hearing there is not the engines themselves, which [arguably might be] shielded from us by the [front and rear booms], but the noise of the jet stream that is fired backwards by the engines, as it hits the air behind the [rear boom]. Because that collision occurs outside of the [putatively] sonically shielded region immediately around the plane, it is free to propagate and so we can hear it.

The picture in @jack action's post 27 shows this jet stream extending beyond/behind the rear 'boom'. The gas is ejected so fast that it is essentially a powerful, incredibly high-speed projectile that laughs derisively at boom regions as it smashes through them at super-supersonic speeds.

 

[russ_watters]

Sound backwards and forwards.There is no limit on the time you get backwards sounds. The sounds played 1 minute before you hear the airplane have been played at a distance of about 2 "sound-minutes", so you'll hear them two minutes after the airplane passes you. Well, in theory, because hearing sound over ~40 km distance is impractical.

How? At the very least, sounds trying to travel away from the plane forward will be overtaken and obliterated by the plane. And it is my understanding that the whole forward arc from the points tangent to the mach cone are part of the mach cone because they are emitted on the cone.

 

[mfb]

How? At the very least, sounds trying to travel away from the plane forward will be overtaken and obliterated by the plane. And it is my understanding that the whole forward arc from the points tangent to the mach cone are part of the mach cone because they are emitted on the cone.

It is overtaken (by the rear shockwave), but the signal is still there. Assuming you don't have some object so blunt and fast that you are really creating a good vacuum over a large range.

The sound simply does not care (in any relevant amount) about other sound or shockwaves nearby.