Can we hear a supersonic plane?

[A.T.]

Like I said several days ago, the reason that the sound in front of the craft is propagating at mach 2 is because that is THE SPEED OF SOUND at that point in the medium.

The front shock continuously propagates at the speed of the aircraft, because it continuously has the aircraft behind it pushing the air. A shock from a short explosion at the side has no such reason to propagate at the speed of the aircraft.

 

[fizzy]

This is what I think the wave fronts should look like.

Backward propagation can probably be approximated as spherical with significant doppler shift. Forward propagation is at the speed of the aircraft so all forward waves are coincident.

Now I have put a straight line between the two which is clearly not accurate but gives an idea. I can't be bothered to make a research project out if this .

All depends upon correct calculation of that part. Immediately around the nose cone it will be the mach bow wave, and I suspect this is the case going out from there too.

If there is some space between the lines, as in my clumbsy hand drawn graphic, that would leave open the possibility for backwards sound. I'm NOT suggest that is the case with this graphic. I don't believe that is the case. But I don't think we can be more definative without doing some serious work, which would be interesting but I don't have the time to do.

 

[fizzy]

The front shock contentiously propagates at the speed of the aircraft, because it contentiously has the aircraft behind it compressing the air. A short explosion shock at the side has no such reason to propagate at the speed of the aircraft.

That's betting thinking. But the shock wave is not just directly in front. It is the mach cone. Everything inside the mach cone is going progressively more slowly as a non linear function of the ( normal? ) distance from the cone surface. The shock front will reduce to propagating at mach as we look further back along the cone.

Sound just inside the cone will be severely doppler shifted. Sound propagating perpendicular to the line of flight will not; and backwards will be doppler shifted to lower.

I still don't see much proof or demonstration of a reversed sound effect but it is not possible to be definitive on the basis of hand-waving thought exercises such as this thread.

 

[A.T.]

This is what I think the wave fronts should look like.

Try figure 4 here:
https://www.researchgate.net/publication/230702229_Reproduction_of_Virtual_Sound_Sources_Moving_at_Supersonic_Speeds_in_Wave_Field_Synthesis

 

[boneh3ad]

What is R and T , not much point is posting undefined terms.

I'm guessing that T is temperature. What do you imagine the temperature of the air 1 cm in front of the nose cone is? What does this tell us about the pressure there. What does that imply about the speed of sound at that point?What is making the air move at mach 2 just in front of the nose cone ? It is not in contact with the plane. It is the air pressure behind it which makes it move at mack 2. Sound is a compression wave. This speed is, by definition, the speed of sound at that point in the medium.

$\gamma$ is the ratio of specific heats, $R$ is the specific gas constant and $T$ is the absolute temperature.

I don't have to imagine what the temperature is 1 cm in front of the tip. If it's a sharp tip, that is part of the free stream and has the same pressure, temperature, and zero velocity as the free stream. If it's a rounded tip or sharp with a large cone angle, it depends on the stand-off distance of the resulting bow shock.

At any rate, it doesn't tell us anything. The plane is moving through the air faster than information about that plan can propagate forward since information about the plane's passing is carried on sound waves. This is why shockwaves form, in essence. For a bow shock, the tip actually pushes some air forward with it, which is moving subsonic relative to the plane, and the shock forms just beyond that region of relative subsonic flow (which is now moving supersonic relative to the free stream).

The speed of sound is always $a =\sqrt{\gamma R T}$. The speed of sound cannot, by definition, be Mach 2.

 

[fizzy]

This was linked here already I think:

https://www.researchgate.net/publication/230702229_Reproduction_of_Virtual_Sound_Sources_Moving_at_Supersonic_Speeds_in_Wave_Field_Synthesis

"...the wave field contains a component carrying a time-reversed version of the source’s input signal...”

This is an interesting, yet simple paper. You will note that neither the maths nor the simulation with an array of static devices will produce the difference in pressure and hence the speed of sound caused by truly moving physical sound source. They have a uniform speed of sound throughout, even when supposedly analysing a super sonic source.

This is not physically realistic and I suspect that the negative frequencies they found are a result of this short-coming of the model.

 

[fizzy]

The speed of sound cannot, by definition, be Mach 2.

What is the DEFINITION of the "speed of sound" you are referring to?

 

[fizzy]

$\gamma$ is the ratio of specific heats, $R$ is the specific gas constant and $T$ is the absolute temperature.

I don't have to imagine what the temperature is 1 cm in front of the tip. If it's a sharp tip, that is part of the free stream and has the same pressure, temperature, and zero velocity as the free stream. If it's a rounded tip or sharp with a large cone angle, it depends on the stand-off distance of the resulting bow shock.

At any rate, it doesn't tell us anything. The plane is moving through the air faster than information about that plan can propagate forward since information about the plane's passing is carried on sound waves. This is why shockwaves form, in essence. For a bow shock, the tip actually pushes some air forward with it, which is moving subsonic relative to the plane, and the shock forms just beyond that region of relative subsonic flow (which is now moving supersonic relative to the free stream).

The speed of sound is always $a =\sqrt{\gamma R T}$. The speed of sound cannot, by definition, be Mach 2.

Since there is a movement of air "just beyond" the high pressure region just in front of the nose there must be some "information" ahead of the plane. This information is traveling at precisely the same speed as the plane.

 

[boneh3ad]

What is the DEFINITION of the "speed of sound" you are referring to?

The speed at which acoustic waves pass through a medium.

Since there is a movement of air "just beyond" the high pressure region just in front of the nose there must be some "information" ahead of the plane. This information is traveling at precisely the same speed as the plane.

Yes, because in that case, the plane is pushing some of the air along with it, which creates a thin layer of air in front of the nose that is moving at the same speed (or very close) as that of the plane. Information (in the form of pressure waves) propagate through this thin layer until they reach the shock, and help maintain its formation when they become a part of it. For a sharp tip, this doesn't happen and the tip essentially pierces the air as it passes through.

I'd suggest you pick up a text or two on this field if you are really this interested. It may clear a few things up for you. You can get https://www.amazon.com/dp/0486419630/?tag=pfamazon01-20 for very cheap. https://www.amazon.com/dp/0072424435/?tag=pfamazon01-20 is also very good and a bit more accessible, albeit quite a bit more expensive.

 

[fizzy]

Thanks for the refs.

So shock waves are not "sound waves" and travel faster than the "speed of sound". So when we hear the crack of an F15 fly past we should remember that we are not hearing a sound ! The roar that follows is sound but not the boom.

Seems like we need another terms for the speed of propagation of a pressure wave when it is not "acoustic".

So the pointed object does not push air forwards, does not produce the same pressure and velocity gradient and thus no shock wave.

 

[jack action]

The air closer to the nose cone gets progressively heated and pressurised and becomes more dense. This means that the speed of sound nearer to the cone is slightly higher than just a little further in front. Hence effect of sound energy 'piling up'.

If an object moves at Mach 1, and emits a pressure wave at point $A$, they will both reach point $B$ at the same time. If the object emits another pressure wave at point $B$, then it adds up to first one, hence the 'piling up'.

Now pressure wave emission is a continuous phenomena ($B = A +dx$) rather than discrete ($B = A +\Delta x$), so the 'piling up' effect is instantaneous and continuous.

The reason why the front shock wave gets more and more in front of the object as its speed gets greater than Mach 1, it is because the local temperature in front of the object increases due to the pressure increase. This has the effect of increasing the local speed of sound ($\sqrt{\gamma RT}$), hence why it takes longer for the pressure waves to "pile up" (i.e. further in front of the object). So the pressure increase doesn't promote the "piling up", it prevents it.

Like I said several days ago, the reason that the sound in front of the craft is propagating at mach 2 is because that is THE SPEED OF SOUND at that point in the medium.

The speed of sound is the speed of sound, which is Mach 1 by definition. Mach 2 is the speed of the sound source, which is not the same thing.

Why do you think that if a plane moves at Mach 0.1 or Mach 0.5, the speed of sound is Mach 1, but when the plane speed exceeds Mach 1, the speed of sound adjust to the speed of the plane?

So shock waves are not "sound waves" and travel faster than the "speed of sound". So when we hear the crack of an F15 fly past we should remember that we are not hearing a sound ! The roar that follows is sound but not the boom.

Shock waves are the accumulation of pressure waves. Pressure waves travel at the speed of sound. But the "accumulation" can travel at a speed faster than the speed of sound (i.e. the speed of the moving source). Shock waves are not sounds, but they emit sounds, so you are hearing a sound. For example, an explosion is not a sound, yet you still hear it because it is a sound source.

 

[fizzy]

The speed of sound is the speed of sound, which is Mach 1 by definition.

Since it is a variable quantity there is no useful meaning to THE speed of sound. It can only be used in that way if you use it as a shorthand for the speed of sound in standard conditions: dry air STP etc.

None of this contradicts my description of the shock wave moving faster than the regionally local "speed of sound" because the speed of propagation is increased by the pressure in front of the aircraft.
Engineer's toolbox says:

The velocity at which a small disturbance will propagate through the medium is called Acoustic Velocity or Speed of Sound.

So if we are to reserve "speed of sound" for small amplitude pressure waves I should substitute the speed of propagation of the pressure wave but the essense of what I said is correct.

You cannot say that air which is not in contact with the metal nose is being "pushed along" and therefore some part of its speed does not "count". Clearly all the air except the static thin film which is in contact with the metal is being accelerated by the air pressure behind it. It is a pressure wave and its speed is the speed of propagation of that pressure wave. No handwaving, word games or adjustments required.

 

[boneh3ad]

So shock waves are not "sound waves" and travel faster than the "speed of sound". So when we hear the crack of an F15 fly past we should remember that we are not hearing a sound ! The roar that follows is sound but not the boom.

Shock waves are a degenerate form of a sound wave (or pressure wave, same thing). When a pressure wave moves through air, it subtly changes the properties of the gas, and in particular, it raises the temperature slightly. That slight increase in temperature means that there is a slight increase in the speed of sound in that region just behind a pressure wave. For most waves, the amplitude is not large enough for this to make any real difference; the wave will dissipate long before any piece of the downstream wave catches up to the peak. However, if the wave is strong enough, then it can "break" when the wave "catches up with itself". If you plotted the pressure over time, the wave front would be vertical at that point, and if the wave continued to "catch itself" it would become a multi-valued function, which can't physically happen. When the wave breaks, it does so by forming a shock, which have similar but different properties than the weak waves that never break. You can hear them both under the right circumstances, so it is still "sound". The reference I linked earlier, Elements of Gasdynamics, has a pretty good discussion of this, as does Linear and Nonlinear Waves that I linked even earlier in the discussion.

So the pointed object does not push air forwards, does not produce the same pressure and velocity gradient and thus no shock wave.

No, it still produces a shock wave. It produces an attached oblique shock wave, which is what creates a Mach cone. If the cone angle is too steep or the tip is blunt, then you get a detached bow shock that exists slightly in front of the tip (how far depends on a lot of factors) and that shock eventually bends around and forms a Mach cone just like a normal oblique shock would.

Since it is a variable quantity there is no useful meaning to THE speed of sound. It can only be used in that way if you use it as a shorthand for the speed of sound in standard conditions: dry air STP etc.

Just because something is variable doesn't mean it isn't clearly definable quantity. The speed of sound is the speed at which pressure waves move through a medium at a given set of conditions.

None of this contradicts my description of the shock wave moving faster than the regionally local "speed of sound" because the speed of propagation is increased by the pressure in front of the aircraft.

The shock is moving faster than the speed of sound in the medium into which it is propagating, which is completely fine. However, the shock wave is still moving less than the speed of sound in the medium through which it is propagating. That is the important difference.

So if we are to reserve "speed of sound" for small amplitude pressure waves I should substitute the speed of propagation of the pressure wave but the essense of what I said is correct.

There is no difference there. Acoustic waves are pressure waves, and their properties obey the same rules regardless of amplitude until they break.

You cannot say that air which is not in contact with the metal nose is being "pushed along" and therefore some part of its speed does not "count". Clearly all the air except the static thin film which is in contact with the metal is being accelerated by the air pressure behind it. It is a pressure wave and its speed is the speed of propagation of that pressure wave. No handwaving, word games or adjustments required.

Of course I can, because that is exactly what is happening. Because the air just in front of a blunt tip is subsonic relative to the plane, the influence of the plane can be felt for some distance upstream of the plane. However, since the plane is moving supersonic relative to the air it is moving into, there must be a shockwave that forms because the plane and the thin layer of air it pushes along with it will reach the undisturbed medium faster than pressure waves can propagate out further in front.

 

[rootone]

Well I'll I heard was just a compressed 'crack' like sound, then a couple of echoes.
I would be shocked and upset if I heard music aboard the plane playing backwards.

 

[A.T.]

Well I'll I heard was just a compressed 'crack' like sound, then a couple of echoes.

Yeah, you said that already. The supersonic plane would have to generate distinct loud sound events like gun shots, before passing the detector.

 

[woody stanford]

You have to be in the right position to be passed by the Mach cone and hear the boom. You also don't hear the sonic booms from the supersonic bullets you fire.

Ok so let me see if I get this straight. Since they go vertically, you are in the mach cone so that's why you don't hear a sonic boom? This makes sense because I ve been around transsonic rockets before and I thought I was going crazy. lol

Thank you so much.

 

[A.T.]

Since they go vertically, you are in the mach cone so that's why you don't hear a sonic boom?

Yes, for you to hear the boom the object has to pass you after it went supersonic.