# Interval between double sonic booms

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The notion of phase gives me a problem because it implies some natural frequencies of oscillations. Isn't the shock wave more random than that? There must be turbulence but are the modes well defined if it's possible to have a spectrum of wavelengths which can interfere in some way. Trouble is that the verbal handwaving that I have read in the popular discussions doesn't do any more than say 'this or that' happens.
That is not a very good explanation. This is better, I think: If the initial wave is an impulse of finite duration and finite attack and decay then there will be a spectrum consisting of an infinite number of frequencies which rolls off at 1/ttransitions. The filtering (dispersion) effect of the propagation on the conical wave will suppress the high frequencies and only the very low frequencies will survive as far as the ground.

It would be interesting to know if there is an audio recording of the shock wave in the close vicinity of the plane.
Supersonic shock waves are frequent with high velocity rifles but the initial explosion could interfere with hearing just the shock wave

My motivation is that the shock wave looks like a step function and at the point it becomes regular (linear) sound we can look at the Fourier decomposition of that shape as a boundary condition. I think the step center defines a surface of constant phase for all component waves.. I'm being a little loose here but I think you follow. I also glanced at Cerenkov radiation as a model and think it may work to save effort at "reinventing the wheel."
Supersonic shock waves are frequent with high velocity rifles but the initial explosion could interfere with hearing just the shock wave
Does a supersonic rifle give different sound than .22? Let us not forget that a bullwhip (I guess that really is true...)

Summary: Can you tell the length of the aircraft by the interval>

Yesterday afternoon I heard (and so did every bird in the district) a very loud, low frequency, double boom which was very vigorous and I suspected all sorts of things but then I thought "double boom!!" and (engaging smartarse mode) I informed my wife that it was only a sonic boom. I was later proved right. Apparently, a Typhoon fighter had been ordered to race to the scene of a civilian aircraft and to accompany it back to Stanstead (UK) airport.
Now here's the thing. Yesterday's two booms were very close together and I remembered a few occasions in my teens when Concord was being tested in the West Country. Those booms were wider spaced iirc. I then thought that the interval between the booms would be strongly related to the length of the craft. A Typhoon is 16m long and Concord was 62m long. So the boom boom yesterday would have been about 1/4 the interval that I remember from the past. The actual speed of the aircraft would (I suspect) not be as important as that would only affect the angle of the shock wave and there would be some trigonometry involved. Does that sound reasonable or is my memory (50 years) just dodgy?
Back in the Space Shuttle era double sonic booms were frequently discussed when the Orbiter was in sight of the landing zone. A good example of this is at elapsed time of 03:01 in this youtube video:

I'm assuming the "double boom" is a "plus" step followed by a "minus" step. Yes?

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I'm assuming the "double boom" is a "plus" step followed by a "minus" step. Yes?
I don't think that's a good way to look at it; you are implying a 'blow' at the front and a 'suck' at the back. But the lowest suck pressure (highest negative) pressure possible is Zero. The (positive) pressure at the front is enormous and the effect at the back is similar.
As far as I can see. the transitions both from air to plane and plane to air must produce positive shockwave pressure. I would look upon it as the air coming together at the back with a clang and that would generate positive pressure. My experience has been that both booms are of equal amplitude (for what it's worth).

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My motivation is that the shock wave looks like a step function and at the point it becomes regular (linear) sound we can look at the Fourier decomposition of that shape as a boundary condition. I think the step center defines a surface of constant phase for all component waves.. I'm being a little loose here but I think you follow. I also glanced at Cerenkov radiation as a model and think it may work to save effort at "reinventing the wheel."

Does a supersonic rifle give different sound than .22? Let us not forget that a bullwhip (I guess that really is true...)
It would be hard to make a control experiment.
Also, the power is so much less than a plane and the dispersion effects would not be heard at the same distance. It would not ‘scale’.

As far as I can see. the transitions both from air to plane and plane to air must produce positive shockwave pressure. I would look upon it as the air coming together at the back with a clang and that would generate positive pressure. My experience has been that both booms are of equal amplitude (for what it's worth).
I recommend a quick look at

Apparently the "N" wave is positive -negative slope -positive, hence its name. The Max over-pressure ever measured was 144 psf (1 psi.... it seems too small, doesn't it?) so you could easily have a negative "gauge" pressure that low

And just for semantic clarity: by definition a shock wave is always moving supersonic speed I think?. The sonic front that describes the boom at the ground is then not really a shock wave even though its point of contact with the earth moves along at the supersonic speed of the plane.

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I agree. If there was an actual shock wave on the ground there would be a net movement of air.
The N wave appears to be a measurement on the ground and, by then, the shock wave has been dissipated and what remains is a low frequency sound pulse with fairly low peak to peak air pressure variation.
Nowhere can the absolute air pressure be less than zero. Descriptions of this need to use the term ‘gauge pressure’ to avoid confusion, I think.

I agree. If there was an actual shock wave on the ground there would be a net movement of air.
The N wave appears to be a measurement on the ground and, by then, the shock wave has been dissipated and what remains is a low frequency sound pulse with fairly low peak to peak air pressure variation.
Nowhere can the absolute air pressure be less than zero. Descriptions of this need to use the term ‘gauge pressure’ to avoid confusion, I think.
The term " shock wave" is used very carelessly in the literature. What I still don't understand at all is how far from the aircraft does the true shockwave persist. Centimeters ? hundreds of meters? You can see the "N' pressure profile in some of the color enhanced schlieren imagery;

Gold Member
What I still don't understand at all is how far from the aircraft does the true shockwave persist. Centimeters ? hundreds of meters?
I have the same problem. The only thing one can work on is those images which show a curved wavefront extending to a bit less than the size of the plane. Beyond that, the wavefront is 'straight' and that suggests that there is no change beyond the curved bit. The only alternative is to assume that the transition from shock wave to sound wave is way beyond what any of the photographs show. We can't be the only ones with this question so I have to conclude that the transition region is quite small.

I have some experience of ships' wakes and I can say that when I have been 'hit' by the wake of large ships, passing within several ship lengths (in deep water) I have not been aware of being pushed to one side; it's been largely up and down (scary at times) motion. So that implies to me that the 'shock wave' region is limited.

cjl
I'm assuming the "double boom" is a "plus" step followed by a "minus" step. Yes?
As has already been stated, but I feel like elaborating, it's actually usually a positive step, followed by a linear negative slope, then another positive step. This is called an "N-wave", for obvious reasons. The magnitude of the overpressure is very small, since it is basically just a sound wave at the point it reaches the ground.

Interestingly, the reason for this shape is because a positive step following another positive step will tend to catch up to the front one, while a negative pressure change will tend to spread out. As a result, all the smaller positive steps coming off of various parts of the aircraft will tend to coalesce, while the negative pressure gradients will tend to spread out and smooth out until you get that characteristic N shape. You can see this very well here.

sophiecentaur
cjl
The term " shock wave" is used very carelessly in the literature. What I still don't understand at all is how far from the aircraft does the true shockwave persist. Centimeters ? hundreds of meters? You can see the "N' pressure profile in some of the color enhanced schlieren imagery;
The actual shock only really persists as far from the plane as the flow itself is impacted. An oblique shock (by definition) causes the flow to change direction, so as soon as you're far enough away that the flow direction is basically unchanged through the wave, you're at the region where you have a sonic boom rather than a shock.

EDIT: Interestingly, this means that the shock will both be significantly stronger and persist farther from the plane when it is making more lift, such as when it is pulling a high-G turn, even if the airplane's shape and mach number are identical, simply because it has to affect more air in a larger volume around the plane.

sophiecentaur
Gold Member
The actual shock only really persists as far from the plane as the flow itself is impacted.
A brilliant observation. It's something I have seen (a classic demo) of the wind in front of a loudspeaker at high sound levels. The wind is in the positive direction - momentum transfer directly to the air molecules - but the return flow is due to the pressure from all around. A candle flame is constantly pushed away.
There must be similar circular motion in the shock wave - I guess that's the quoted turbulence idea.
the shock will both be significantly stronger and persist farther from the plane when it is making more lift,
Another good observation!

russ_watters
Mentor
Are you saying that the waves you hear are due to individual local 'explosions'? I understood that the booms are caused by a pair of conical waves going past your ears.
It's not "explosions"; many concentric circles are just a simple way to describe it, and may help here. But think about the geometry of this. When the cone reaches you, the plane is past you. So where was the plane when the sound incorporated into that part of the cone was released?

It must be the shortest distance the sound can travel, which is the perpendicular/closest point of approach.

sophiecentaur
Gold Member
It's not "explosions"; many concentric circles are just a simple way to describe it, and may help here. But think about the geometry of this. When the cone reaches you, the plane is past you. So where was the plane when the sound incorporated into that part of the cone was released?

It must be the shortest distance the sound can travel, which is the perpendicular/closest point of approach.
Yes - I get it now. It's isolated pulses involved and the nearest point is the source of the main part of the energy. The conical wavefront is formed by many contributing spherical wavelets though. It's a diffraction mechanism. The period of the pulse received is very long and it is only the lowest frequency parts of the spectrum that make it to the ground. Almost more of a 'woomph" than a "bang".

It must be the shortest distance the sound can travel, which is the perpendicular/closest point of approach.
This is fundamentally true but oversimplified. Waves from parts of the path before and after the distance of closest approach also contribute to the front (they can do that only because the plane is supersonic). The ones that do it coherently are Gaussian distributed along the path with a sigma proportional to the wavelength centered at the point of closest approach. I have worked this out ( in Eikonal approximation) and will write it up when I can find a few hours. Obviously the long wavelengths then sample more of the path and so are more prominent in the "boom" front. The amplitude of the boom falls off like √ (distance of closest approach) because the wave is essentially a cylindrical wave.
This has been a great question!

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sophiecentaur