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

[powermind]

Hi,
Suppose the police car moves faster than sound's speed and runs away from the person on the street. Will the person hear the siren?

Regards,

 

[Borek]

Did some cleaning, as old discussion sidetracked. Old thread is here: https://www.physicsforums.com/showthread.php?t=732514

Please keep answers to original question and discussion on the sonic boom separated.

 

[voko]

The person will hear the sonic boom.

 

[A.T.]

The person will hear the sonic boom.

If the car only moves away from the person, as stated, the person will not hear the boom. If it initially moves towards the person and passes it, the person will hear the boom and only after the boom the siren.

 

[voko]

If the car only moves away from the person, as stated, the person will not hear the boom.

How is that possible? The shock wave propagates in all directions regardless of the motion of the object causing it.

 

[A.T.]

The shock wave propagates in all directions regardless of the motion of the object causing it.

You hear the boom when the Mach cone passes you. If the car is moving away from you, as it passes the speed of sound, you are always inside that cone, and are never passed by it.

 

[powermind]

Borek, this is similar to the light, is not this?
The light speed is not affected by the speed of its source too.

 

[Nugatory]

Borek, this is similar to the light, is not this?
The light speed is not affected by the speed of its source too.

Very different, because the speed of sound is the same relative to the air, while the speed of light is always the same relative to all observers. To see the difference, consider the experience of someone moving through the air at less than the speed of sound - he if he emits a flash of light, it will expand away from him at an equal speed in all directions, but if he emits noise, he'll always be closer to the forward-moving sound wave than the backward-moving one.

All sorts of other differences flow from this. For example, you can travel faster than sound, but you cannot travel faster than light.

 

[voko]

You hear the boom when the Mach cone passes you. If the car is moving away from you, as it passes the speed of sound, you are always inside that cone, and are never passed by it.

The Mach cone is an idealization based on the assumption that the supersonic body has always been supersonic. You are breaking that assumption when you say "as it passes the speed of sound". As it passes the speed of sound, it will generate a shock wave in all directions, including those in the rear hemisphere.

 

[A.T.]

As it passes the speed of sound, it will generate a shock wave in all directions, including those in the rear hemisphere.

Isn't that shock wave a superposition of only those wave fronts which move forward? If yes, why would they start moving backward?

 

[voko]

Isn't that shock wave a superposition of only those wave fronts which move forward? If yes, why would they start moving backward?

As the the rearmost point of an accelerating body passes the speed of sound, it will create a spherically propagating shock wave. In the rear hemisphere, there will be nothing for it to be in superposition with, so it will propagate spherically.

 

[sophiecentaur]

I think it's correct to say that the 'Shock Wave' only exists quite near the speeding object. It is the region where the air is pushed forwards at greater than the speed of sound at that point. Once out of the influence of the object / plane / car the 'sound wave' (boom) just travels at the normal speed of sound in air.

 

[A.T.]

I think it's correct to say that the 'Shock Wave' only exists quite near the speeding object. It is the region where the air is pushed forwards at greater than the speed of sound at that point. Once out of the influence of the object / plane / car the 'sound wave' (boom) just travels at the normal speed of sound in air.

The question is: Will you hear a boom, if you were behind the plane as it passed sound speed?

 

[sophiecentaur]

This is almost an unanswerable question. If it went past, you would have heard it anyway. If it sets of in a direction away from you, you will hear the event of it starting off, accelerating rapidly and 'breaking the sound barrier'.. Just as it crosses Mach 1, I think the sound wave will leave in a spherical pattern, which will get to you, even behind the event. So, one way or another, I think you will hear 'something. The boom would be a very low frequency, I think (sub woofer stuff).

 

[cjl]

As the the rearmost point of an accelerating body passes the speed of sound, it will create a spherically propagating shock wave. In the rear hemisphere, there will be nothing for it to be in superposition with, so it will propagate spherically.

No, I don't believe this is even close to correct. You typically get expansion waves (which dissipate rather quickly) off the rear of an object as it passes the speed of sound, not shock waves, and you would not hear the sonic boom. The compression waves would only occur on the front of the object, and would propagate forwards and to the sides. Obviously, this is highly geometrically dependent, but I can't think of an object shape that would generate a rearward-traveling shock as it passed the speed of sound.

 

[boneh3ad]

You do often get shock waves coming off the back of supersonic objects, but they aren't spherical. They are simply oblique shock waves. It depends on the shape of the object, though. Ultimately, if you were directly behind an object that was impulsively accelerated to supersonic speeds, you would not hear the sonic book, as you wouldn't have the pressure wave associated with the shock crossing your ear. You would still hear the siren on the car because sound propagates at the speed of sound relative to the propagation medium, not relative to the source, so it would still propagate backward from the initial point of generation at 343 m/s, which would be much greater relative to the car.

 

[voko]

No, I don't believe this is even close to correct. You typically get expansion waves (which dissipate rather quickly) off the rear of an object as it passes the speed of sound, not shock waves, and you would not hear the sonic boom.

As the rear accelerates beyond the speed of sound, there will be a discontinuity in the pressure after it. That is a shock wave by definition.

 

[voko]

You do often get shock waves coming off the back of supersonic objects, but they aren't spherical.

I was just using the simplest geometry possible - one rearmost point.

They are simply oblique shock waves. It depends on the shape of the object, though. Ultimately, if you were directly behind an object that was impulsively accelerated to supersonic speeds, you would not hear the sonic book, as you wouldn't have the pressure wave associated with the shock crossing your ear.

Please refer to my previous post. Explain how the pressure discontinuity mentioned there would disappear.

You would still hear the siren on the car because sound propagates at the speed of sound relative to the propagation medium, not relative to the source, so it would still propagate backward from the initial point of generation at 343 m/s, which would be much greater relative to the car.

So the acoustic disturbance from a supersonic siren propagates back just fine, but the shock from a supersonic siren does not?

 

[boneh3ad]

I was just using the simplest geometry possible - one rearmost point.

If the object came to a point at the back and was moving with no incidence angle to the flow, you would have a conical shock wave attacked to that back point.

Please refer to my previous post. Explain how the pressure discontinuity mentioned there would disappear.

A conical shock wave as previously mentioned would still account for a discontinuity. That said, a discontinuity need not occur behind an object traveling at supersonic speeds as you seem to have asserted. If, for example, the object is traveling at an angle of incidence greater than the exit angle of that trailing point, you would have an expansion for one half of that conical trailing wave, which is not discontinuous. Take, for example, this image of a diamond-shaped object moving at supersonic speeds:

The trailing oblique shocks are not there because a pressure discontinuity must necessarily exist, but because the supersonic flow must turn back into itself, requiring an oblique shock.

Also, if you check out the example here, you can see what I was talking about where you can get an expansion wave coming off the rear of a supersonic object. This works for essentially any supersonic shape, but is simply the easiest to describe for simple shapes like diamonds. A sphere, for example, would still have a similar character.

So the acoustic disturbance from a supersonic siren propagates back just fine, but the shock from a supersonic siren does not?

Essentially yes. The shock is attached to the body and is a result of the disturbance created when the body moves through the air. Air must get out of the way or be otherwise redirected, and since the forward-traveling disturbances generated by the body can no longer outrun or even keep up with the body itself as it continues outputting disturbances, these disturbances essentially "pile up" and form shock waves. It is essentially the result of the Doppler shift when the source is moving at the speed of sound and the equation describing the shift becomes singular. That is the shock wave.

The siren is similarly continuously outputting a sound, and in front of the vehicle, you wouldn't hear it coming until the shock was already past you. Behind it though, it would still be audible, albeit much lower in frequency due to the Doppler shift.

 

[voko]

If the object came to a point at the back and was moving with no incidence angle to the flow, you would have a conical shock wave attacked to that back point.

As I said earlier, a conical shock wave is an idealization where the supersonic body is assumed to have been supersonic forever. It is the product of the interference of the spherical shock waves excited by the body continuously during its infinite flight.

I am talking about the case when a subsonic body becomes supersonic and the shock wave system forms for the first time. The first, so to speak, spherical shock wave has nothing to interfere with in the rear hemisphere, so it will propagate as a spherical shock there.

I am not commenting the rest of your message because you are obviously talking about a different regime.

 

[A.T.]

I am talking about the case when a subsonic body becomes supersonic and the shock wave system forms for the first time. The first, so to speak, spherical shock wave has nothing to interfere with in the rear hemisphere, so it will propagate as a spherical shock there.

How exactly does the first shock form, if not by piling up disturbances that travel forward? Why should the shock wave propagate backwards, if it is formed by piling up only those parts of the waves which travel forward?

 

[voko]

How exactly does the first shock form, if not by piling up disturbances that travel forward? Why should the shock wave propagate backwards, if it is formed by piling up only those parts of the waves which travel forward?

See #22.

 

[boneh3ad]

As I said earlier, a conical shock wave is an idealization where the supersonic body is assumed to have been supersonic forever. It is the product of the interference of the spherical shock waves excited by the body continuously during its infinite flight.

I am talking about the case when a subsonic body becomes supersonic and the shock wave system forms for the first time. The first, so to speak, spherical shock wave has nothing to interfere with in the rear hemisphere, so it will propagate as a spherical shock there.

I am not commenting the rest of your message because you are obviously talking about a different regime.

The problem is that your assumption here about the nature of shocks is incorrect. The conical shock is not an idealization that requires the supersonic body to have been supersonic forever. Decades of schlieren and shadowgraph images have shown conical and other oblique shocks forming on surfaces that get accelerated from stationary to supersonic and it still forms an oblique shock.

A subsonic body becoming supersonic is no different. It is simply a time-varying system, but the shock ultimately comes from the same source. The body, even when subsonic, is essentially sending information about itself through tiny pressure/density waves that radiate away from the body continuously. In a subsonic flow, these waves are still there but propagate fast enough that a given wave is never caught by its subsequent waves (or at least not before significant amounts of dissipation has occurred). As you speed up, the waves on the front side are emitted closer together than they were until eventually they get so close that they start to interact with the waves emitted before them. This is when compressibility starts to become important in the flow.

Once you reach the speed of sound, these waves can no longer get out of the way of the ones emitted subsequently and the resulting finite-amplitude waves "break" and become a shock wave. This shock wave becomes increasingly oblique as the velocity continues to increase. Wikipedia actually has a very nice set of animations showing this based on a point source that emits a series of discrete waves.

Stationary ($M=0$):

Subsonic ($M<1$):

Sonic ($M=1$):

Supersonic ($M>1$):

where $M$ is the Mach number.

There is never and will never be a shock wave in the rear of the moving point source, as those waves are not actually "piling up". On a more realistic shape like a diamond, there is a shock at the rear because the air leaves the surface at a nonzero angle relative to the free stream and must be turned back in line with the free stream. Usually this turning involves compression, and information about the compression cannot propagate upstream since it is traveling faster than the speed of sound, so a shock must accomplish the compression and flow turning.

There is no discontinuity that forms solely as a result of a body accelerating past the speed of sound. If and when a discontinuity does form, it is a result of the supersonic compression required behind the body. At exactly $M=1$, the "weak" shock would be spherical, but it would quickly dissipate, as it isn't really a shock, but on the cusp of forming a shock, and it would be spherical in the sense that its "front end" would be located at the rear of the object and the center would be at the location where the object started.

 

[voko]

The conical shock is not an idealization that requires the supersonic body to have been supersonic forever. Decades of schlieren and shadowgraph images have shown conical and other oblique shocks forming on surfaces that get accelerated from stationary to supersonic and it still forms an oblique shock.

A conical surface is infinite. Anything which is said to be conical is an idealization just because of that. Any image of a physical process captures a finite spatial extent, so imagery cannot substantiate claims about infinite surfaces.

Supersonic ($M>1$):
[PLAIN]http://upload.wikimedia.org/wikipedia/commons/e/e4/Dopplereffectsourcemovingrightatmach1.4.gif[/QUOTE]

This illustration shows a shock wave system made of shock waves propagating spherically; in particular, it shows a spherical front propagating backward, which I have been talking about.

There is never and will never be a shock wave in the rear of the moving point source, as those waves are not actually "piling up".

You misunderstand what "shock wave" means. To quote Wikipedia: "Shock waves are characterized by an abrupt, nearly discontinuous change in the characteristics of the medium. Across a shock there is always an extremely rapid rise in pressure, temperature and density of the flow". It has nothing to do with "piling up", nor with "breaking of finite-amplitude waves".

 

[A.T.]

[PLAIN]http://upload.wikimedia.org/wikipedia/commons/e/e4/Dopplereffectsourcemovingrightatmach1.4.gif[/QUOTE]
This illustration shows a shock wave system made of shock waves propagating spherically;

To me, it shows sound waves propagating spherically. So yes, you will hear sound behind the object. Just as you do when the object is slower than sound.

in particular, it shows a spherical front propagating backward,

A single spherical front propagating backward? Where?

which I have been talking about.

You were talking about a "sonic boom" that is heard behind the object. If you interpret all those those spherical fronts propagating backwards as individual "shock waves", then you would hear many individual "booms". What those spherical fronts propagating backwards mean to me, is a continuous sound.

Let me ask you this way: 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]

A conical surface is infinite. Anything which is said to be conical is an idealization just because of that. Any image of a physical process captures a finite spatial extent, so imagery cannot substantiate claims about infinite surfaces.

I said nothing about infinite surfaces. You are making that leap. Obviously nothing is infinite in the real world. I think we both know that, as do most people reading this, so I see no reason to nitpick like that. It adds nothing to the discussion.

This illustration shows a shock wave system made of shock waves propagating spherically; in particular, it shows a spherical front propagating backward, which I have been talking about.

No, the blue circles are not shock waves. They are infinitesimal-amplitude sound waves. When they all coalesce at the front, that is where the shock wave forms. Imagine the blue lines as the peaks of a sinusoidal sine wave if it helps. Behind the source they have a lower frequency and in front they have a higher frequency. When the source reaches the speed of sound, the peaks in front have infinite frequency (zero period) and sit on top of each other, forming a shock.

You misunderstand what "shock wave" means. To quote Wikipedia: "Shock waves are characterized by an abrupt, nearly discontinuous change in the characteristics of the medium. Across a shock there is always an extremely rapid rise in pressure, temperature and density of the flow". It has nothing to do with "piling up", nor with "breaking of finite-amplitude waves".

I am 100% clear on what a shock wave is, and it absolutely does have to do with the interaction of many infinitesimal waves to form a finite-amplitude wave. See, for example, Liepmann and Roshko chapters 3 and 4. It has a nice coverage of wave propagation in a fluid and how those waves can become shocks.

The short description is that if you have a small disturbance propagating through a fluid like a sound wave, you can essentially plot it as a small pressure (or density) pulse. Sound waves are so tiny in amplitude that they typically do not appreciably affect the speed of sound in the propagation medium and travel at what is essentially constant speed. However, when you have a number of waves that are close together and constructively interfere, they can grow to a finite amplitude large enough to appreciably change the speed of sound in the medium, and the speed in a perfect gas like air tends to increase with the increase in pressure (due to the accompanying temperature increase). This means that peaks tend to start catching up with themselves and their leading edges eventually form a vertical, multivalued line, at which point the wave is said to break. This is the genesis of a shock wave. Yes, it has (approximately) discontinuous jumps in properties across the wave, but the wave itself is generated from the coalescence of many small-amplitude waves. I can't find any good images to illustrate this. If I get time later, maybe I will throw some together in Matlab and post them to show what I mean.

To me, it shows sound waves propagating spherically. So yes, you will hear sound behind the object. Just as you do when the object is slower than sound.

Yes, this is the key point here. They are sound waves propagating spherically, not shock waves.

 

[.Scott]

Here are two images that might assist in the conversation.
This first onet shows shockwaves originating from trailing edges of a missile. So shockwaves are not limited to areas that are more obviously compressed by the missile geometry.

http://quest.nasa.gov/aero/events/mars/picture2.jpg

This second one shows a shockwave triggered from a rocket launch. If you've seen videos of rockets passing through the right kind of atmospheric conditions, you have seen a variety of shockwave patterns evolve as the rocket accelerates through higher and higher Mach numbers.

What I don't ever remember is a sonic boom being picked up by the microphones at the launch site.

 

[voko]

I said nothing about infinite surfaces. You are making that leap. Obviously nothing is infinite in the real world. I think we both know that

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.

No, the blue circles are not shock waves. They are infinitesimal-amplitude sound waves.

Please describe how those sound waves are generated.

I am 100% clear on what a shock wave is, and it absolutely does have to do with the interaction of many infinitesimal waves to form a finite-amplitude wave.

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.

 

[voko]

What I don't ever remember is a sonic boom being picked up by the microphones at the launch site.

A typical launch vehicle goes supersonic at 7-8 km altitude. It is off sideways by a few km, too. I do not think a shock wave can propagate that far.

 

[russ_watters]

Voko, you are getting some fabulous help here and you need to start working with these guys and accepting what they are saying instead of fighting them every step of the way. 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.

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.

 

[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.