Interval between double sonic booms

[sophiecentaur]

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’.

 

[hutchphd]

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

https://www.af.mil/About-Us/Fact-Sheets/Display/Article/104540/sonic-boom/
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

 

[hutchphd]

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.

 

[sophiecentaur]

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.

 

[hutchphd]

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;

 

[sophiecentaur]

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.

 

[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]

The actual shock only really persists as far from the plane as the flow itself is impacted.

Great; there's the answer.

while the negative pressure gradients will tend to spread out

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]

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]

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".

 

[hutchphd]

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!