Can we hear a supersonic plane?

[CalcNerd]

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.

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I suspect it is not. Air is not elastic ie there comes a point when the pressure simply compresses the air beyond any elastic limit and produces heat. A 120+ dB (I suspect the sound is much higher, but even 120dB would exhibit this effect) sound/sonic wave will simply crush out a 60 dB conversation. I would like you to provide some type of theoretical argument otherwise. If we were talking electrical signals, I would be on board with your reasoning. However, air reaches a compression limit where it turns into heat instead of allowing another signal to ride on top of this sonic boom that you seem to believe can carry information from inside of the aircraft.

 

[mfb]

I would like you to provide some type of theoretical argument otherwise.

You are the one suggesting some additional effect. Where is your theoretical argument?

 

[Nidum]

Worth a read

 

[CalcNerd]

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My argument again relies upon the obvious (for me, anyway). You are trying to capture information on the other side of (or thru) a sonic wave front (Shock wave). As I alluded to earlier, the air is compressed beyond its sound transmission range into a heating range ie acoustic heating where the air molecules cannot resonate fast enough and are simply crushed together by a sonic wave. I can see no way that you can provide any mechanism to put information on a wave form that is cropped off by thermal upper limit ie the air will only resonate at some upper frequency (speed of sound), beyond that it just booms and heats on the intensity of the sonic wave ie it has a maximum value (wiki, not a great source) of 190 dB. Of course this value drops off as the wave front travels away from the plane. However, simple math on a limit is 190 + anything (your sound wave/voice) = 190 db. The tail sonic wave boom is this limit of information (I am still at a loss of how you propose to do a frequency analysis and capture the information on the other side of a sonic wave front).
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While Jack Action provided sound and pressure waves as two separate examples, they are actually the same example, just at different scales. Sound is simply a pressure wave of a far lower scale. I am stating that the air cannot theoretically carry any information once it is compressed by a sonic boom other than energy information. A spectrum analysis of any exotic form will not recover sound information inside the aircraft cabin ie you will not be able to listen to their music. (we are restricting our argument to sound waves, not laser measurements of the sound perturbation on their cabin wall).
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So I am simply asking you to provide your theoretical solution to overcome the above hurdle. I don't see or seem to understand what I have stated is not obvious. Where is the flaw in my logic.

 

[mfb]

The shockwaves of planes at the relevant distances (10+ meters, where the shockwave meets the sound from the cabin) should be far away from 190 dB. Maintaining a perfect vacuum in a disk with 10 meter radius would require a power of at least 20 GW (31 MN at ~700 m/s), even if we ignore overpressure ahead of the aircraft. That is completely unrealistic, even the most powerful engines just give 100-150 kN thrust.

Why did you link to binoculars?

 

[CalcNerd]

Deleted binoculars. Was going to respond to another thread and didn't delete.
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The shockwaves of planes at the relevant distances (10+ meters, where the shockwave meets the sound from the cabin) should be far away from 190 dB.

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The sound inside the cabin needs to be captured through the shockwave, doesn't it?
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Maintaining a perfect vacuum in a disk with 10 meter radius would require a power of at least 20 GW (31 MN at ~700 m/s), even if we ignore overpressure ahead of the aircraft.

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Where did I say anything about a perfect vacuum (or any vacuum)? But since you bring it up, the aircraft does leave a vacuum in its wake (and you are correct, it is not anywhere close to 10 meters in radius, it is what creates that small tail sonic wave front, with the energy content of some ratio of the engine energy as you surmise), and that vacuum plays into my argument as well. Sound doesn't carry through a vacuum.

 

[mfb]

The sound inside the cabin needs to be captured through the shockwave, doesn't it?

What does "captured" mean? The sound can travel outwards (and forwards as seen from the ground), a bit later the shockwave passes through it.

If we let the sound be emitted 5 meters in front of the end of the aircraft, and consider the part emitted in a 45° angle forwards (as seen from the ground), then the sound hits the shockwave at a distance of 25 meters from the flight path of the mach 2 aircraft.

Where did I say anything about a perfect vacuum (or any vacuum)?

The ~190 dB value corresponds to it.

 

[CalcNerd]

If we let the sound be emitted 5 meters in front of the end of the aircraft, and consider the part emitted in a 45° angle forwards (as seen from the ground), then the sound hits the shockwave at a distance of 25 meters from the flight path of the mach 2 aircraft.

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How in the world do you come up with this? The sound hits that shockwave much closer than 25 meters. I suspect we should pick an aircraft for reference (it seems that you are referencing a common diagram on the web, the true sonic cone envelopes as tightly as possible). However that sound is also sandwiched between the two shock waves, so you have a very brief amount of information that you can gather. I concede that iff you can maintain a sound sensor between the two shock waves, maybe there is a conceptual window to listen into the music inside the cabin. That window is the time distance of the length of a clean aircraft (in feet)divided by its feet / second speed. A sample calculation reveals that a 50 foot F-16 traveling at 850 mph (1250 ft/sec) has a sonic window of 1/25th of a second. Could you make out what song that pilot was listening to? That is a very brief window to capture anything. Keeping up with the aircrafts sonic shadow is not how I envisioned your solution. I believe the implied solution is to capture your information from behind the 2nd sonic tail boom.
Do you have such a solution?
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As far as 190 dB, that is the maximum value of noise possible (according to wiki). That noise is when the air is compressed in front of an aircraft and it cannot move out of the way fast enough, hence a sonic boom.

 

[mfb]

How in the world do you come up with this?

Geometry. But I made a mistake, the value is actually 108 m.

Using v=340 m for the sound (it cancels out in the distances) sound and shockwave hit each other 450 milliseconds after the sound is emitted, 108 meter forwards and 108 meter outwards compared to the sound emission point. The airplane, before emitting the part of the shockwave that hits the sound, moves 54 meters, which needs 79 milliseconds. The shockwave from the tail of the aircraft then travels 121 meters, which needs 356 milliseconds.

If you disagree, find a faster way the shockwave can reach the sound.

However that sound is also sandwiched between the two shock waves

Repetition won't make it right.

Do you have such a solution?

That solution is what we are discussing the whole time?

As far as 190 dB, that is the maximum value of noise possible (according to wiki).

Am I arguing with a Wikipedia article?

 

[A.T.]

How? At the very least, sounds trying to travel away from the plane forward will be overtaken and obliterated by the plane.

Imagine being right under the plane, already inside the cone, in the right picture:

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.

Why the whole forward arc? Only the parts emitted at 90deg - alpha form the cone.

 

[Bystander]

Let's back up a bit and think about the acoustics of projectile motion; is there anything beyond the sonic boom from near misses by bullets?

 

[A.T.]

Let's back up a bit and think about the acoustics of projectile motio

That misses the point. Bullets do not generate well defined ordered sound events that could be heard in reverse.

 

[arydberg]

I suggest an experiment. Go look at a paddiling duck. They travel faster than the velocity of surface waves in water. Thus they put out a v shaped wave. Now you need to make a rythemtic disterbence on the surfave of the water and move it at a velocity faster then the surface waves and you will see the answer.

 

[DrDu]

I was thinking that for the problem at hand maybe one shouldn't focus so much on the shockwave of airplanes but on how to model an ideal supersonic sound source. Theoretically simplest is probably an infinitely thin airfoil whose curvature is changing slightly in positive and negative direction. There even exist analytical solutions in the supersonic region called Ackerets formula. But as long as the airfoil is flat, there will be no sound or shockwave at all. Looking now at the special situation that the sound consist of two short clicks separated by time t, the relative order in which the two click will be heard by an observer will be different whether the observer is in front or behind the flying airfoil. So yes, in principle music can be heard backwards. The situation is not different from the order by which two firecrackers will be heard which are fired at different times at different locations.

 

[boneh3ad]

That misses the point. Bullets do not generate well defined ordered sound events that could be heard in reverse.

Neither do planes, for that matter.

There's some good and some bad in this discussion. Sound and pressure waves are the same things but people get confused because of the different magnitudes typically involved. Shocks are nonlinear phenomena, and can't form in a linear medium. When a sound wave interacts with a shock, it is very unlikely that it will come out the other side unchanged. Most likely the wave will undergo some degree of additional attenuation because shocks are highly dissipative. They wouldn't necessarily be completely destroyed, though.

Also, you can certainly hear sound behind the final boom. It's going to sound substantially quieter than the boom itself, but it will be there, especially if it was emitted from a region downstream of the final Mach cone such as by the engines on a fighter plane.

Finally, there's no need to argue about shock angles. There's a simple geometric explanation for the angles of Mach cones. The Mach angle is:
$$\mu = \arcsin\left(\dfrac{1}{M}\right)$$

 

[A.T.]

Neither do planes, for that matter.

Supersonic fighter jets can for example fire their cannons, in two clearly distinguishable burst (e.g. different number of shots). If the plane then passes a detector close by, that detector would first detect the sonic-booms(s), and then the cannon sounds in reverse order.

 

[boneh3ad]

Supersonic fighter jets can for example fire their cannons, in two clearly distinguishable burst (e.g. different number of shots). If the plane then passes a detector close by, that detector would first detect the sonic-booms(s), and then the cannon sounds in reverse order.

Literally any sound, constant or not, will be detected after the sonic boom due to the limitations of sound speed in the medium. The observer would just hear a mix of the gun firing both in reverse and forward briefly before hearing it all forward, just like any sound.

 

[Jlister]

What about a piezoelectric speaker traveling in the direction of its plane & with a surface that could travel at mach 2 plus a little bit? Aside from being materially impossible.

 

[A.T.]

The observer would just hear a mix of the gun firing both in reverse and forward briefly before hearing it all forward

Why would he hear the same shots multiple times? To clarify: Both burst are finished before the plane passes him. And I'm talking about the gun sounds, let him fire blanks for simplicity.

 

[fizzy]

"Sound waves are linear to a good approximation, there is no destruction going on."Sound may be linear under normal, everyday situations but it will not be linear under extreme conditions like the bow wave of a supersonic aircraft.
What you are trying to suggest is that we should be able to record the sonic boom and pick out the police siren in the recording. I don't believe that for a minute.

As for playing backwards, nothing is heard upstream of the sonic cone ( let's limit this to one sonic boom from the nose for simplicity. ) An observer on the ground , or any other non-axial position of observation will hear sound from the aircraft once it has passed and they are BEHIND the sonic cone. At this point the aircraft is going away from the observer, fast.

There is NO sound coming towards the observer from behind ( in the direction from which the plane arrived ). AFAICS, this whole idea of sound playing backwards, is based on the simplistic and inappropriate 'spherical' wave-fronts which do not apply to a supersonic sound source.

There is a strage idea here that sound is left behind the plane, traveling in forwards direction. The only sound moving forwards contributes to the shock wave and any sound information is lost.

[EDIT]

I've just seen A.T's comment #45
https://www.physicsforums.com/threads/can-we-hear-a-supersonic-plane.881162/page-3#post-5540053

This diagram puts the 'spherical' waves in their correct context. I do not see how anyone can conceive of hearing sounds in a reverse order. The older waves always arrive first.

 

[fizzy]

I like the idea of firing the cannon a lot better than the supersonic ghettoblaster.

If the plane fired it's cannon whilst over the observer ( he is in front of the sonic cone ) , he would never hear those shots. Neither backwards, not forwards.

He can only hear shots fires after the shockwave has passed.

 

[andrewkirk]

The following is the best I've been able to come up with so far, as a practically feasible experimental demonstration of the backwards sound phenomenon:

A plane traveling forwards at Mach 2 fires three exploding shells backwards, at speeds of Mach 1.2 relative to the plane, at times t, t+1, t+3, each programmed to explode after time T, which is the minimum time such that the explosion would be far enough away from the plane to not endanger it.

The shells explode behind the rear boom, at times t+T, t+T+1, t+T+3, and in each case is at the same displacement vector from the plane at the time of the explosion. So we can consider those explosions as part of the supersonically moving phenomenon or system of the plane.

The intervals between explosions, in the reference frame of the plane, are 1 second, then 2 seconds.

But for an observer on the ground that is well in front of the location of the last explosion, the explosions are heard at intervals 2 seconds, then 1 second. That is, they are heard in reverse order.

Because the shells were traveling subsonically prior to exploding (at Mach 2 - 1.2 = 0.8), there is no sonic boom of the shells to complicate the analysis.

In the above scenario, the backwards pattern of shells is heard after the boom.

If the shells were instead fired forwards, a ground observer in front of the plane would hear the explosions in reverse order before the boom, but the analysis would be complicated by having to consider what effect the sonic boom of the shells themselves (which are traveling at Mach 3.2) had on the sound wave of their explosions.

 

[fizzy]

This highlights the basic problem of the reverse play idea. You need to introduce a contrived means to have a secondary source of sound propagating in all directions behind the plane, including forwards. This will not happen with the plane as the source of the original sound. This does not provide a means to suggest that the firing the planes cannon would be heard in reverse playback.

Firing the cannon seems to give the most useful conceptual framework for examining how sound will propagate from a supersonic aircraft.

I see no credible explanation of how wave-fronts emanating form the plane could arrive at an observer in reverse order.

 

[A.T.]

This diagram puts the 'spherical' waves in their correct context. I do not see how anyone can conceive of hearing sounds in a reverse order. The older waves always arrive first.

The diagram shows the exact opposite, of what you claim it shows: If the supersonic plane passes very close to the detector, the youngest signal (smallest circle, emitted most to the left) will reach the detector first. Thus the signals are detected in reverse of the emission order.

Maybe an animation can help you:
https://upload.wikimedia.org/wikipedia/commons/e/e4/Dopplereffectsourcemovingrightatmach1.4.gif

 

[nsaspook]

http://pastebin.com/D4MsBftY

Is this what you mean? I found this on another discussion elsewhere on this subject.

 

[DrDu]

This highlights the basic problem of the reverse play idea. You need to introduce a contrived means to have a secondary source of sound propagating in all directions behind the plane, including forwards. This will not happen with the plane as the source of the original sound. This does not provide a means to suggest that the firing the planes cannon would be heard in reverse playback.

Firing the cannon seems to give the most useful conceptual framework for examining how sound will propagate from a supersonic aircraft.

I see no credible explanation of how wave-fronts emanating form the plane could arrive at an observer in reverse order.

In my previous reply, which seems not to have caught little attention, I pointed out, that the theory of thin supersonic airfoils is basically the same as that of sound generation. Specifically a very thin blade which is either vibrating or maybe simply tilting (modulated with the song we want to hear backwards) may be a very good source of sound especially since an ideally thin, flat and untilted blade won't emit a supersonic boom.
Edit: The very point is that in this setting, the hydrodynamic equations can be linearized and these linearized equations are hyperbolic differential equations. The most important consequence is that sound can only propagate in the region bounded by the Mach cones from the trailing and leading edge. So there will be no sound emitted in the direction opposite to the motion of the airfoil.

 

[fizzy]

Yes, thanks, this image does help see where the misunderstanding lies. The wavefronts are not spherical ripples propagating like ripples on a pond. This animation will produce no sonic boom, there is no shock wave. What you have here is the wake of boat, not a supersonic aeroplane.

All the those segments inside the cone and traveling forward do not exist. They are not left trailing the craft they are compressed into the shock wave in front of it. They are part of the Mach cone.Clearly the sound pressure wave in front of the aircraft is not propagating at 332 m/s, it is traveling at the speed of the aircraft ! Many commenters seem to think that the "speed of sound" is some universal constant.
These simplistic ripples do not exist like that when you have a hard physical object thrust through the air at mach 2. The speed of sound increases with pressure. Clearly the pressure just in front of the nose cone will not be one atmosphere !So, yes, the animation is helpful in showing just where the misconceptions arise. These kinds of simplistic representations are useful in describing superposition of small disturbances in a uniform medium but there are limitations to where they can be applied.

 

[A.T.]

How would the bangs from the cannon propagate if not spherically?

All the those segments inside the cone and traveling forward do not exist.

Why not?

 

[fizzy]

Amazing ! You quote me but cut of half the paragraph which explains it and then come back with "why not?"

"All the those segments inside the cone and traveling forward do not exist. They are not left trailing the craft they are compressed into the shock wave in front of it. They are part of the Mach cone."

The pressure wave in front of the craft is traveling at mach 2 , some way behind it , sound travels at mach 1 . Clearly propagation is not equal in all directions as must be assumed to get spherical wave fronts.

 

[DrDu]

Section 9.2 of this book contains a formula for the sound emitted by a moving point source:
https://www.win.tue.nl/~sjoerdr/papers/boek.pdf

 

[mfb]

All the those segments inside the cone and traveling forward do not exist. They are not left trailing the craft they are compressed into the shock wave in front of it. They are part of the Mach cone.

How can they reach the shock wave in front of it if they are emitted in the middle of the aircraft?

 

[jack action]

I wrote my point of view in an earlier post, which did not create much discussion, except for saying that pressure and sonic waves are the same but of different magnitude ... which was my point.

If pressure waves can't passed one another, thus accumulating until they make a shock wave leading to a sonic boom, how can anyone think that sonic waves will react otherwise than accumulate in front of the moving emitting source and create their own «mini» (because they are of much lower magnitude) sonic boom?

How can they reach the a shock wave in front of it if they are emitted in the middle of the aircraft?

Why would that matter? If the source is emitting directly outside the plane, then the shock wave will be created at that point (middle of the plane). If the sound travels inside the plane (inside air moves with plane, hence M < 1, no shock waves inside) before reaching the front and go outside, then the shock wave will be in the front of the plane.

What I was trying to do with my earlier post was to demonstrate that the shock wave due to pressure waves is a different phenomena (aerodynamics) from sonic waves (sound) and they can be treated apart and they don't have to go together.

Furthermore, I agree with @boneh3ad when he states that pressure waves (aerodynamic source) and sonic waves (sound source) can cross path with each other without affecting their order, even a sound wave crossing a shock wave (not its own, but one created by another source, whether aerodynamic or by a sound emitted). Though, it will affect its speed (when they cross, pressure & temperature increase, therefore speed of sound increases too) and magnitudes are modified due to reflection phenomena (but never to the point of completely eliminating either one of the waves).

 

[fizzy]

Section 9.2 of this book contains a formula for the sound emitted by a moving point source:
https://www.win.tue.nl/~sjoerdr/papers/boek.pdf

Thanks doc, looks like a useful book.

Consider a point (volume) source of strength Q(t) (the volume flux), moving subsonically along the
path x = x s (t) in a uniform acoustic medium. The generated sound field is described byWere you intending that to be relevant to this discussion ?

 

[fizzy]

How can they reach the shock wave in front of it if they are emitted in the middle of the aircraft?

What is doing the emitting? An object ( ghetoblaster, cannon, ... ) itself moving at mach II.

Sound waves still will not propagate forwards in nice little spherical waves when being emitted by a source moving at twice the speed of sound. The constructed thought experiment is still being treated like ripples on a pond in a situation where this is not applicable.

 

[DrDu]

Thanks doc, looks like a useful book.

Consider a point (volume) source of strength Q(t) (the volume flux), moving subsonically along the
path x = x s (t) in a uniform acoustic medium. The generated sound field is described byWere you intending that to be relevant to this discussion ?

They comment in the footnote on the derivation being also applicable in the supersonic case and we assume the medium to be uniform (air), don't we?
Maybe the book they cite by Morse and Ingard "Theoretical Accoustics" contains more on this.
I must say that I am a bit puzzled. Their equation 9.16 clearly shows that the solution is a superpostion of spherical "Coulomb" potentials. On the other hand
for a thin airfoil, the pressure variation seems to vanish outside the Mach cone:
https://www3.nd.edu/~atassi/Teaching/ame 60639/Notes/supersonic_airfoil.pdf
So it seems to me that this is a consequence of the source term Q(t) having a special distribution in the supersonic case.
Chapter 9.1 of the book seems highly relevant for that case, too.