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Similar to how the 3D relieving effect will change the shockwave angle (see above), will this same effect change the shock angle and strength further away from the body? As a shock goes through different temperature air and density, the shockwave strength will be affected. Will the 3D effect also change the angle/strength?

Imagine you have a cone going supersonic like the one above. As the shock gets further from the body, it will continue in a straight line. However, shocks aren’t just 2d, they continue out in a cone shape.

Similar to how if a sphere was emitting sound in all directions, the sound would be forced to spread out as it got farther from the sphere. I’m asking if this same effect happens to shockwaves, considering shocks are in a 3d cone shape.

(If the question is hard to understand, comment and I’ll do my best to improve it; I found this hard to explain.)

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    $\begingroup$ Think of the cone not in isolation but as a combination of the cone itself plus the deadwater it carries along. I don't know if that helps because I found it hard to isolate the real question here. $\endgroup$
    – Peter Kämpf
    Commented Jul 7 at 7:14
  • $\begingroup$ @PeterKämpf I don’t blame you, I wasn’t able to explain this very well. Imagine you have a 2d circle. It is emitting sound waves in all directions. In this case for the sake of explanation, when the sound waves travel off, they go in a straight line and don’t interact at all. Because each of those waves were emitted at a slightly different angle (because it was a circle) at some distance wouldn’t those waves start to separate? I’m asking if that same thing applies to the (oblique) shocks that extend from a body. $\endgroup$
    – Wyatt
    Commented Jul 7 at 14:30
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    $\begingroup$ It's a single, circular wave which is emitted. Amplitude will drop with distance, but other than that it will stay unchanged as it radiates out. Since it is radially symmetric, I do not understand why you think something should separate here. $\endgroup$
    – Peter Kämpf
    Commented Jul 7 at 18:32
  • $\begingroup$ @PeterKämpf Right, but each part of that single wave was emitted at a slightly different angle. Imagine you were standing on a part of the theoretical circle, and you throw a ball straight up. Now move over a tiny bit and do the same thing (still on the circle). Those balls would be on trajectories leading away from each other, right? Sorry if this is still confusing, I can't explain this for the life of me. $\endgroup$
    – Wyatt
    Commented Jul 8 at 0:15
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    $\begingroup$ The imaginary rays of sound start to "separate" instantly as they propagate, not "at some distance". There is not a break or gap in the expanding circular/spherical wave front because there are an infinite number of rays and between every two rays that are separating, there are an infinite number of rays that fill in the gaps. Still, the density of the rays (which are just mathematical models - there aren't real sound rays) decreases as the wave front expands and that decreasing density models how the intensity of the wave front decreases as it expands. $\endgroup$
    – Todd Wilcox
    Commented Jul 8 at 2:49

2 Answers 2

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Is the cone an infinite cone? If the cone is finite -- like all real cones -- then there will ben an expansion fan off of the end of the cone that will interact with the shock and will bend it.

Remember, the shock at an angle turns the flow by a certain angle. If the flow does not need to turn the same amount, then the angle of the shock will change.

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  • $\begingroup$ Hmm, okay. I’ll copy/paste what I said to Mr. Kämpf here, because I didn’t explain my question properly. Imagine you have a 2d circle. It is emitting sound waves in all directions. In this case for the sake of explanation, when the sound waves travel off, they go in a straight line and don’t interact with each other at all. Because each of those waves were emitted at a slightly different angle (because it was a circle) at some distance wouldn’t those waves start to separate from each other? I’m asking if that same thing applies to the (oblique) shocks that extend from a body. $\endgroup$
    – Wyatt
    Commented Jul 7 at 16:14
  • $\begingroup$ (Let me know if that didn’t make sense) $\endgroup$
    – Wyatt
    Commented Jul 8 at 1:52
  • $\begingroup$ The circular pressure wave that comes from a disturbance does not come at an angle, it goes in all directions equally. The reason they can coalesce into a Mach wave is because the disturbance is moving. It is the combination of the forward speed with the radial wave speed that causes the waves to build up in front of the disturbance and spread out behind. Again, this is for an infinitesimal disturbance -- not for a cylinder or sphere. $\endgroup$
    – Rob McDonald
    Commented Jul 8 at 4:56
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It sounds like the thrust of your question is about whether the wave front will begin to develop 'gaps' like in your analogy of the ball being thrown up from different angles. The issue is that the wave front is not a discrete object like the balls, but rather the force moving through the objects (which in this case are air molecules). If you were talking about photons from the sun, then you may see gaps between the individual photons that radiate out in a sphere as you move very far out, but because the shock-wave is transmitted through the movement of atmosphere, without significant displacement of the molecules that are transmitting the force, the shock-wave will behave more like a continuous line in space with infinitely many points all spreading out. As such, we would not perceive any spacing between the points, just a net depreciation of amplitude as you move further from the origin of the shock-wave.

In the case of oblique shocks, I am not sure if you could have constructive/destructive interference from multiple incidence points of the geometry of the object that is moving. That may appear to be gaps, but I think they would also behave more like lines/regions in 3d space - growing in scale as they propagate away from the origin.

I hope I haven't misunderstood what you were getting at.

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