The police car moves faster than the speed of sound? Sonic boom.

[russ_watters]

Please describe how those sound waves are generated.

Simply put, the sound waves being discussed are the disturbances of the air caused when an object moves. They are the "whooshing" sound you hear when you are in a moving vehicle.

 

[boneh3ad]

If we both know that , the perhaps it is time that you stopped talking about conical shock waves at the time of the shock system's formation.

I will not stop talking about that because that is exactly what happens, and this has been demonstrated experimentally, numerically, and analytically over decades of aeronautics research.

Please describe how those sound waves are generated.

As russ_watters has said, they are generated by virtue of an object moving through the air. Something has to move the air out of the way, and that is the force of the surface pushing through the air. This forces is transmitted through the fluid as pressure waves.

Any real sound wave has a finite amplitude and any real sound wave can be considered as a superposition of many (infinite) sound waves. Your definition of a "shock wave" is not specific enough to distinguish it from a broader phenomenon.

Any real sound wave has finite amplitude and any real gas has viscosity, which is dissipative. If your amplitude is small enough, it can be treated as if it is infinitesimal. After all, even loud sounds like jet engines represent overpressure of several orders of magnitude smaller than ambient pressure and you don't see shock waves constantly propagating spherically away from jet engines. Basically, if the amplitude is "small enough", any dissipative effects are going to damp out the nonlinear growth effects in the sound waves and you aren't going to see a shock forming. You need a much larger disturbance than that to have what are typically called finite-amplitude waves.

As it turns out, despite the fact that things in the real world are finite, they are also dissipative, and the combination tends to allow sound waves to be treated as mathematically infinitesimal and the physics in almost every observed situation agrees.

And sure any real sound wave can be considered a superposition of infinitely many component waves. Of course, so can literally any other function. That's the Fourier series. That is irrelevant here, though.

My definition of a shock wave is fully capable of distinguishing it from an ordinary sound wave. For starters, an ordinary sound wave is not multivalued (discontinuous) as is a shock wave. Of course if you want to really get nitpicky about it like you were earlier, a shock wave in real life is not actually discontinuous. It merely changes over such a tiny length scale that it can be treated as such. In reality, shock waves have a finite thickness (a handful of mean free paths of the fluid in question) and properties vary smoothly across that distance.

 

[A.T.]

My definition of a shock wave is fully capable of distinguishing it from an ordinary sound wave.

Regardless of the "sound wave " vs. "shock wave" question, voko's claim is that the rear observer will hear a "sonic boom". It would be nice if he would clarify what "hearing a sonic boom" means to him, by answering my question:

If you were behind the object, could you identify a distinct time point when the "sonic boom" reached you? If yes, how? Would the continuous sound you hear anyway suddenly become louder?

 

[boneh3ad]

Regardless of the "sound wave " vs. "shock wave" question, voko's claim is that the rear observer will hear a "sonic boom". It would be nice if he would clarify what "hearing a sonic boom" means to him, by answering my question:

If you were behind the object, could you identify a distinct time point when the "sonic boom" reached you? If yes, how? Would the continuous sound you hear anyway suddenly become louder?

And I think the reason for him taking that position is a result of his misunderstanding of shock waves, when they form and why they form.

 

[boneh3ad]

To illustrate what I was talking about with a wave "breaking", I threw this figure together over lunch. It basically just shows a finite-amplitude density pulse propagating through air at 4 different times. You can see that the areas of greater amplitude travel faster and essentially catch (third image) and pass (fourth image) the points in front of them on the wave. In reality, as the third image comes to pass, it forms a shock wave rather than forming the physically intractable fourth image since the same point in space can't have two separate density values.

For reference so this doesn't seem like black magic, I calculated this from the speed of sound in air at sea level based on density variations using the acoustic wave equation for a gas with variable wave speed.

 

[voko]

Your mistake is a common one because of how pop culture describes the phenomena, but rather than just accepting correction, you are piling new wrongness on top of the old.

I do not think you have really tried to understand what I have been saying. I specifically do not discuss whatever happens during the steady supersonic flight.

The wiki has a section on perception that discusses your misconception:

http://en.m.wikipedia.org/wiki/Sonic_boom

Among other things, it mentions:
1. You can't hear it if you are inside the cone (such as in the plane)
2. There is no special extra boom upon crossing the threshold.

I am talking about the brief period of formation of the shock system. There is no "cone" at that time, so I cannot see how your statement 1 could apply to this case.

I never spoke about any "special extra boom" so I cannot see how your statement 2 would be relevant. Just for the record, I could not find that statement in the referenced text.

Do you perhaps qualify the onset of sonic boom effects at the formation of the shock system as "special extra boom"?

 

[voko]

I will not stop talking about that because that is exactly what happens, and this has been demonstrated experimentally, numerically, and analytically over decades of aeronautics research.

Please cite any source demonstrating "conical shock waves" during the brief period of formation of the shock system. Please be specific.

As russ_watters has said, they are generated by virtue of an object moving through the air. Something has to move the air out of the way, and that is the force of the surface pushing through the air. This forces is transmitted through the fluid as pressure waves.

And when that pressure wave's amplitude is equal to or greater than the pressure of ambient atmosphere, you would still call it a "sound wave"?

My definition of a shock wave is fully capable of distinguishing it from an ordinary sound wave.

Frankly, you wrote so much that I am not sure at this stage how you define a "shock wave". Really, I am not nitpicking. Could you please provide a concise and unambiguous definition of a "shock wave"? Thank you.

 

[voko]

Regardless of the "sound wave " vs. "shock wave" question, voko's claim is that the rear observer will hear a "sonic boom". It would be nice if he would clarify what "hearing a sonic boom" means to him, by answering my question:

If you were behind the object, could you identify a distinct time point when the "sonic boom" reached you? If yes, how? Would the continuous sound you hear anyway suddenly become louder?

Let's put this back into the original context. The question was whether an observer would hear a siren from a police car speeding away from the observer supersonically.

Two situations are possible.

1. The car has passed the observer while already supersonic.

2. The car becomes supersonic away from the observer.

In situation one, I think we all agree that the observer must have heard a sonic boom (provided the observer was close enough to the car).

In situation two, the sonic boom must have started propagating while the car was away. My claim is that initially it propagates omnidirectionally, so the observer will hear it (same condition). Whether it will be louder than the sound heard previously, I cannot say, but I do think the observer should detect some change in the character of the sound.

I hope that answers your questions.

 

[russ_watters]

Do you perhaps qualify the onset of sonic boom effects at the formation of the shock system as "special extra boom"?

Yes, that's what you have claimed. It isn't identical to my points 1 or 2, it is a combination of both: If you were correct that a spherically propagating shock wave traveled backwards from the airplane at the moment the plane passed the speed of sound - inside the cone, the pilot would hear it because he is inside the cone.

Please cite any source demonstrating "conical shock waves" during the brief period of formation of the shock system. Please be specific.

The transition period is not brief, it takes a fairly significant amount of time. The shock waves that form on the plane form at places where the flow reaches the speed of sound first; at bulges. This happens when the plane as a whole is still significantly below the speed of sound (100+ km/hr). See the bottom diagram here:
http://en.wikipedia.org/wiki/Transonic

Those shock waves form and then move forward toward the front as the plane accelerates.

And when that pressure wave's amplitude is equal to or greater than the pressure of ambient atmosphere, you would still call it a "sound wave"?

That never happens, even in a shock wave - and trying to split hairs on the definition does not change the science.

Again: you are being argumentative and you need to stop. This isn't a "lets argue to see who wins and who is right" situation. This is a situation where you don't know what you are talking about, are making it up as you go along, and need to stop arguing and start learning.

So let's try it this way: from this point forward, you need to start citing sources for your claims or don't make them.

 

[voko]

So let's try it this way: from this point forward, you need to start citing sources for your claims or don't make them.

Please explain what you mean by "claims". Is that anything specific or is that anything I say you disagree with? How can in the latter case I know it is a claim? Shall I submit my posts to you privately for your approval?

 

[boneh3ad]

I do not think you have really tried to understand what I have been saying. I specifically do not discuss whatever happens during the steady supersonic flight.

I am talking about the brief period of formation of the shock system. There is no "cone" at that time, so I cannot see how your statement 1 could apply to this case.

The problem is that steady supersonic flows are not really all that different in this regard to the transient period at the beginning while accelerating. Right as the object passes Mach 1 there would be an locally spherical bow shock at the tip, but as soon as it passes Mach 1, even while still accelerating, that shock is now going to be locally conical. The only thing changing as it continues accelerating is the angle of the cone.

Please cite any source demonstrating "conical shock waves" during the brief period of formation of the shock system. Please be specific.

On the contrary, please cite any source showing that they are not conical. I am contending that the rules governing shock structure are no different while accelerating than they are while moving steadily. Therefore, with the exception of the infinitesimal moment in time where the Mach number is identically 1, the shock is conical. In that brief moment where the object is exactly sonic, the "shock wave" is infinitesimally weak. If you plug Mach 1 into the normal or the oblique shock relations, you get that there is no shock. There is no overpressure, velocity change, temperature change or any other change across this locally spherical boundary, so it makes no sonic boom.

And when that pressure wave's amplitude is equal to or greater than the pressure of ambient atmosphere, you would still call it a "sound wave"?

Do you mean its absolute pressure or its overpressure? Either way whether or not it is a shock wave depends on the character of the wave. Most of the time a wave that compresses the flow an entire 1 atm above ambient pressure will be a shock wave (at M=1.363, if normal). That isn't necessarily the case though, although any such sound wave would almost certainly very quickly degenerate into a shock wave.

Frankly, you wrote so much that I am not sure at this stage how you define a "shock wave". Really, I am not nitpicking. Could you please provide a concise and unambiguous definition of a "shock wave"? Thank you.

A shock wave is a disturbance wave in a medium across which the disturbed properties jump discontinuously (or at least can be treated as such). In the microscopic sense, their formation in the context of supersonic objects moving through air typically results from the small disturbance waves generated by the object in motion constructively interfering until their amplitude is such that the speed of sound can no longer be assumed constant on all points of the wave and the wave distorts, reaches the point where it is multivalued, and becomes a shock wave (see the series of four graphs I posted earlier).

Let's put this back into the original context. The question was whether an observer would hear a siren from a police car speeding away from the observer supersonically.

Two situations are possible.

1. The car has passed the observer while already supersonic.

2. The car becomes supersonic away from the observer.

In situation one, I think we all agree that the observer must have heard a sonic boom (provided the observer was close enough to the car).

Sure they would. They would hear the siren, too. I don't believe anyone has contended that they wouldn't hear a boom in that situation.

In situation two, the sonic boom must have started propagating while the car was away. My claim is that initially it propagates omnidirectionally, so the observer will hear it (same condition). Whether it will be louder than the sound heard previously, I cannot say, but I do think the observer should detect some change in the character of the sound.

I hope that answers your questions.

And this is where we take issue. The sonic boom does not propagate omnidirectionally for the reasons stated earlier in this post. The siren would still be audible, but its frequency would be Doppler shifted significantly lower. As long as that shift doesn't bring the sound waves below the frequency of human hearing, it would be audible.

I see exactly why you are thinking the way you are, and it almost makes sense. The problem is that at exactly Mach 1, the small pressure waves are still spherical, but everywhere except at the very tip of the object, they are moving with enough speed to continue to outrun the wave emitted after them since the supersonic body is not moving fast enough to generate the waves before the previous wave can leave the area. If you think about it, at the very tip, where the vehicle is moving at the exact speed of sound, each wave will be generated on top of the last and you might expect a shock to form. If you move even a fraction of a degree (around the spherical wave front), then you have to factor in a cosine term to the velocity of the emitting body in that direction while the wave front still moves at the same constant speed of sound. In other words, anywhere except at the very tip, the waves are perfectly capable of keeping ahead of those emitted after them. So, at Mach 1, there is no shock, and therefore no sonic boom. Once you bump up to Mach 1.000000000001, a shock would form, albeit very weak and almost normal to the direction of travel, and this shock would be conical.

That never happens, even in a shock wave - and trying to split hairs on the definition does not change the science.

That does happen, and it happens all the time. For example, at work I run a Mach 6 wind tunnel. The ambient atmospheric pressure inside the undisturbed region of the test section is about 0.08 psia. If I put a 7-degree wedge into the flow, the resulting shock wave raises the ambient pressure behind it to 0.21 psia. You could get it a lot higher if you use other shapes so that the wave isn't so oblique, too. For example, we have a miniature Apollo capsule model, and at the very front of that in the same tunnel, the pressure would rise to 3.44 psia, more than 40 times the ambient pressure.

 

[russ_watters]

Please explain what you mean by "claims". Is that anything specific or is that anything I say you disagree with? How can in the latter case I know it is a claim? Shall I submit my posts to you privately for your approval?

The part after "My claim is..." was your claim.

You agreed to the rules of the forum when you signed-up. We don't typically require pre-approval of posts (though it does happen), but we do take action for violations after the fact. Asking me to explain the word "claim" after you used it when making your claim is extremely argumentative, to say the least.

 

[russ_watters]

That does happen, and it happens all the time. For example, at work I run a Mach 6 wind tunnel. The ambient atmospheric pressure inside the undisturbed region of the test section is about 0.08 psia. If I put a 7-degree wedge into the flow, the resulting shock wave raises the ambient pressure behind it to 0.21 psia. You could get it a lot higher if you use other shapes so that the wave isn't so oblique, too. For example, we have a miniature Apollo capsule model, and at the very front of that in the same tunnel, the pressure would rise to 3.44 psia, more than 40 times the ambient pressure.

Fair enough; I wasn't thinking of the high altitude/hypersonic regime.

 

[boneh3ad]

Fair enough; I wasn't thinking of the high altitude/hypersonic regime.

Move an F-15 at Mach 2 at 100 feet off the ground. The pressure rise across the shock will still more than double the pressure versus ambient. As long as the gas isn't rarefied, it will behave at 100,000 feet the same as it does at 10 feet.

 

[russ_watters]

Move an F-15 at Mach 2 at 100 feet off the ground. The pressure rise across the shock will still more than double the pressure versus ambient. As long as the gas isn't rarefied, it will behave at 100,000 feet the same as it does at 10 feet.

The wiki on sonic booms (i think it is linked earlier) says the strongest ever measured for an aircraft was 7,000 pa for an F-4, supersonic at 100 feet.

What am I missing?

 

[voko]

Asking me to explain the word "claim" after you used it when making your claim is extremely argumentative, to say the least.

You used the word in plural and the structure of your sentence led to me believe it would apply to what I would say in future, not what I had said in the past. Now you seem to say that it applies to just one claim that I made in the past. I do not understand what that all means and, frankly, now it seems much easier to ignore this thread rather than risk being "in violation".

 

[boneh3ad]

The wiki on sonic booms (i think it is linked earlier) says the strongest ever measured for an aircraft was 7,000 pa for an F-4, supersonic at 100 feet.

What am I missing?

That may be the maximum overpressure created by the sound measured for the given conditions. The wiki article states that was measured from an F-4 flying at about 100 feet altitude flying just above the speed of sound. It doesn't cite an actual Mach number, but close to Mach 1, the actual overpressure is quite small (25% overpressure for a Mach 1.1 normal shock, for example; less for the oblique shock that would actually form). The overpressure from a faster vehicle at higher altitude would be substantially higher, but it has time to dissipate before reaching the ground where measurements are made, plus the shock becomes increasingly oblique (and therefore weaker) as it intersects the other waves generated by the body.

If they did that same experiment with the F-4 flying at Mach 2 at 100 feet instead of slightly greater than Mach 1, the overpressure would be much larger. It would also probably rupture some eardrums, so they wouldn't do that.

they still have F-15? they can fly 100000 feet? what is that - ionosphere?

The F-15 is still the main air superiority fighter in the USAF since the procurement of F-22's was scaled back for cost reasons. I don't believe anyone has claimed they can fly at 100,000 feet.

 

[A.T.]

Whether it will be louder than the sound heard previously, I cannot say, but I do think the observer should detect some change in the character of the sound.

Ok, "some change in the sound" seems possible. The sound changes all the time during the acceleration due to Doppler shift. But if we don't even know if it gets louder, I wouldn't call it a "boom".

 

[A.T.]

For example, at work I run a Mach 6 wind tunnel.

Do you have some good Schlieren movies of objects passing Mach 1? Ideally slow motion. This one seems to go slightly above Mach 1:

https://www.youtube.com/watch?v=BsIabrtezIQ

I see no distinct shock wave going back. But if it is real time, it might be to fast to see anything.

 

[boneh3ad]

Do you have some good Schlieren movies of objects passing Mach 1? Ideally slow motion.

I don't. My tunnel doesn't have optical access to the tip of models. We use primarily hot-wire anemometry for measurements.

The same lab has another Mach 5 to 8 tunnel with optical access, but we don't have a camera fast enough to capture that startup transient, as it's probably only a matter of microseconds and you would need a camera with a framing rate of about twice the value of the reciprocal of that transient time, so probably in the high kHz or even MHz range. We don't have a high speed camera capable of that.

This one seems to go slightly above Mach 1:

I see no distinct shock wave going back. But if it is real time, it might be to fast to see anything.

It says it is varying from Mach 0.7 to Mach 1. If it passes Mach 1 I'd be a little surprised there on account of the fact that you never see a shock form up at the leading edge. Instead it just has the highly unstable shocks forming along the body characteristic of transonic flow.

 

[boneh3ad]

The closest I have found of a startup shock is this:
https://www.youtube.com/watch?v=iNBZBChS2YI

It isn't nearly fast enough to capture the incident though.

EDIT: This one is even better. Still isn't fast enough framing rate though.
https://www.youtube.com/watch?v=anuuKLyLj3E

 

[A.T.]

The same lab has another Mach 5 to 8 tunnel with optical access, but we don't have a camera fast enough to capture that startup transient, as it's probably only a matter of microseconds and you would need a camera with a framing rate of about twice the value of the reciprocal of that transient time, so probably in the MHz range.

Maybe you know some movies from other labs. I saw some videos of tunnels stating up quickly to supersonic, but there is to much noise (shock waves from the walls?) at Mach 1. What one would need is a slow transition. If there was a shock wave going back, it would move at Mach 2 relative to the camera. This is fast, but hi-speed cameras capture shock waves propagating at Mach 1 relative to the camera, so Mach 2 should be possible to.

 

[cjl]

The wiki on sonic booms (i think it is linked earlier) says the strongest ever measured for an aircraft was 7,000 pa for an F-4, supersonic at 100 feet.

What am I missing?

I believe that's the boom at ground level, while the actual overpressure behind the shock (between the nose of the aircraft and the shock wave) is much, much higher. Obviously, the high overpressures dissipate rather quickly as you go away from the aircraft.

 

[boneh3ad]

Maybe you know some movies from other labs. I saw some videos of tunnels stating up quickly to supersonic, but there is to much noise (shock waves from the walls?) at Mach 1. What one would need is a slow transition. If there was a shock wave going back, it would move at Mach 2 relative to the camera. This is fast, but hi-speed cameras capture shock waves propagating at Mach 1 relative to the camera, so Mach 2 should be possible to.

It wouldn't necessarily be moving at Mach 2 relative to the camera. When you start a supersonic tunnel, the air is initially at rest or approximately at rest relative to the camera. The starting shock then travels through the test section, and does so at the design Mach number as long as it remains a normal shock. If it doesn't (it often doesn't) then it's a little more complicated but it won't be a drastically different speed. This means it is propagating into the stagnant air at the design Mach number, meaning Mach 6 for the tunnel I use, for example, not Mach 12.

Capturing shock motion on video is possible for lower Mach numbers if you have the right equipment. You need a very bright light source to illuminate your image sensor on your camera over such a short duration. You need a very fast camera (generally 10's of kfps), and you need a relatively low Mach number. For example, this paper have a pretty neat schlieren technique detailed in it. You'll notice it was published in 2005, so it wasn't until recently that this was even possible, and even then it was novel and uncommon enough as to be publishable in a relatively well-known journal.

I've also heard of it being done with lasers, but that doesn't generate a movie; it generates a point measurement or a series of time-resolved point measurements. We also did some work here using a focusing schlieren system and measured at 2 MHz, but those were done with photodiodes and, again, were point measurements, not movies.

So yes, it's possible, but not trivial to procure the equipment or cheap, so unless you have a good reason to do it (we don't), then generally you don't do it.

 

[russ_watters]

The overpressure from a faster vehicle at higher altitude would be substantially higher, but it has time to dissipate before reaching the ground where measurements are made, plus the shock becomes increasingly oblique (and therefore weaker) as it intersects the other waves generated by the body.

That's probably it - they don't explicitly say it, but I think the issue that caused my confusion was that they were measuring the pressure at ground level, not the pressure across the shock wave near the plane.

 

[russ_watters]

In any case, I think the question is answered and due to some problems in the thread, it is locked.