Can we hear a supersonic plane?

[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.

 

[fizzy]

On the other hand for a thin airfoil, the pressure variation seems to vanish outside the Mach cone:

Since sound cannot propagate in front of the cone, isn't this always going to be zero, no matter what the form of the supersonic object?
This is why we do not hear anything until the perimeter of the mach cone passes the point of observation.

 

[DrDu]

Since sound cannot propagate in front of the cone, isn't this always going to be zero, no matter what the form of the supersonic object?
This is why we do not hear anything until the perimeter of the mach cone passes the point of observation.

For the front this is obvious, but for the rear?

 

[fizzy]

What do you mean by "the rear".

 

[DrDu]

What do you mean by "the rear".

Have a look at the figure in https://www3.nd.edu/~atassi/Teaching/ame 60639/Notes/supersonic_airfoil.pdf

 

[fizzy]

What do YOU mean by 'rear'? Behind the cone? Behind the plane of the aircraft perpendicular to line of flight? Inside the cone?

I really can't understand what you are trying to suggest.

 

[DrDu]

Sorry. I mean the region with x>c and small y in that figure.

 

[mfb]

The ghettoblaster/cannon is not emitting continuous sound. Let our "music" be composed of the individual gunfires. Each one creates its own pseudo-shockwave (which has a roughly spherical pattern if the sound duration is short enough, because we don't care about the airplane motion during that short period) - but those shockwaves emitted later are ahead of those created earlier. For shockwaves produced early enough, an observer on the ground will hear the later shockwaves first.

 

[fizzy]

mfb, you are still ignoring the fact that you can not model sound produced by the cannon as a spherical wave as it would be if it were stationary. That is the whole point of the confusion here, and the false notion that there is a sound wave propagating forwards behind the aircraft.

 

[fizzy]

Sorry. I mean the region with x>c and small y in that figure.

"On the other hand for a thin airfoil, the pressure variation seems to vanish outside the Mach cone:"

Isn't what you describe INSIDE the mach cone?

 

[DrDu]

Isn't what you describe INSIDE the mach cone?

Maybe I should have written "outside the region between the front and rear Mach cone".

 

[fizzy]

Ok, I don't see this discussion getting anywhere at all. I'm off to do other things.

Interesting post though.

 

[A.T.]

you are still ignoring the fact that you can not model sound produced by the cannon as a spherical wave as it would be if it were stationary.

They don't have to perfectly spherical for the reverse order detection to occur.

 

[mfb]

mfb, you are still ignoring the fact that you can not model sound produced by the cannon as a spherical wave as it would be if it were stationary. That is the whole point of the confusion here, and the false notion that there is a sound wave propagating forwards behind the aircraft.

The extremely fast cannon perturbes the air at a single point of spacetime (let's say it adds more air there from the explosion). Neglecting scattering from the aircraft, what shape do you expect? What breaks the symmetry?
What breaks it so massively that we don't have anything that looks like forward/downward propagation (as seen from the ground) any more?

 

[fizzy]

What breaks it so massively? The fact that the forward propagation is at mach II , not mach I

I have not done the maths on this but I guess that the pressure and density of the air in front of the aircraft has to be that at which the propagation of sound is twice as fast as it is in still air.

So the sphere is elongated. Moreover it is continually stretching not just scaling up in a linear fashion as with the animation posted earlier.

The shock wave is like a continuous explosion. Unlike a thunder clap which propagates and attenuates, the crack of supersonic flight is only a crack for stationary observer. The sharp almost step change in air pressure at the front of the plane continues to emit it's explosive energy as long as the craft is supersonic.

 

[A.T.]

The fact that the forward propagation is at mach II , not mach I

We are not interested in propagation exactly forward, like the bow shock at the very front of the plane. We are interested in gun/explosion sounds generated at the side of the plane propagating sideways with some forward component.

 

[fizzy]

There is a similar shock wave off the leading edge of the wings and a tiny one on the end of the cannon if you want to look at that aspect. ( even if we want to avoid confusing the issue by discussing the explosion of the charge ).

You simply can not pretend that the cannon , moving forwards at mach 2. will but pumping out nice little spherical wavelets propagating omni-directionally at mach 1 .

I can't believe that this discussion is still going on without advancing one iota.

 

[mfb]

I think we get to the main point.

The fact that the forward propagation is at mach II , not mach I

There is not even a forward propagation involved in the single, instant, explosion in the gun.

You imagine a continuous sound source, but we don't have that. Our sound source (gunfire, ghetto blaster, whatever) is not active continuously. It is not an obstacle in the wind (or at least that is not the part we care about).

 

[jack action]

@mfb , @A.T. :

I can hear the music backward now!

Slow, but got there.

 

[A.T.]

You simply can not pretend that the cannon , moving forwards at mach 2. will but pumping out nice little spherical wavelets propagating omni-directionally at mach 1 .

Again, we don't need to assume perfect spheres to get the reverse effect.

You on the other hand, seem to claim that the entire forward hemisphere of the explosion shock will be deformed exactly such that it catches up, and perfectly merges with the shock cone of the plane. That seems the far more unlikely option, and I haven't seen a good reason or evidence for it, just mere assertions.

I can't believe that this discussion is still going on without advancing one iota.

Because you keep repeating the same non-argument: Stating that the explosion shock propagation won't be perfectly spherical, doesn't imply that its entire forward hemisphere will be part of the Mach cone.

 

[DrDu]

Again, we don't need to assume perfect spheres to get the reverse effect.

IMHO, the really interesting point is that you seem to need a strong perturbation for information to leave the conical shell between the front Mach cone and the rear Mach cone. In paragraph 3 they explicitly state that information can't leave the Mach wedge,
https://www3.nd.edu/~atassi/Teaching/ame 60639/Notes/supersonic_airfoil.pdf
although this analysis clearly refers to small perturbations, only.
An explosion, is certainly a strong perturbation while I doubt that a loud speaker in an aerodynamical plane will qualify as a strong perturbation.