So It's Back To First Principles (Part 2)

by the way, there was a PSP car - but only a few seconds of the footage was released

heads turned to the railings impact - they heard it

at this angle the bullet probably would ricochet

Actually I cannot see the top of the railing.

Why not? It is not a wall which stops the sound. It is the wave front of shock wave. And that sound will not stop when the bullet hits the target.

You’re absolutely right to point out that the Mach cone is not a physical wall, and your thinking is on the right track regarding sound propagation.

Clarifying the Concept:

The Mach cone is the 3D shock wave front generated by an object moving faster than the speed of sound (i.e., supersonic). It’s essentially a conical wavefront that forms behind the object and represents where the pressure disturbances (shock waves) from the object arrive simultaneously.

:loud_sound: Why the Sonic Boom Is Only Heard Inside the Mach Cone

  • The sonic boom is the accumulated shock wave front from a supersonic object.
  • The boom is heard only by observers who are inside or directly intersected by this cone, because:
    • That’s the only region where the pressure wavefronts constructively overlap into a shock wave.
    • Outside the cone, no shock front reaches the observer, so no sonic boom is perceived.

:brain: Think of the Mach cone like the “path” that the boom travels along as the object moves.

wait - here the “inside” should mean the 2D conic surface, not the 3D conic volume

:brick: Why It Feels Like a “Barrier”

You’re right: it’s not a wall that stops sound, but rather a boundary of constructive interference:

  • Inside the cone: You hear the sharp “boom” from the shock wave.
  • Outside the cone: You may hear other acoustic phenomena (like regular subsonic sounds if the object slows down), but not the boom.

:arrows_counterclockwise: Does the Sound Continue After the Bullet Hits?

Yes, sound continues to propagate from the moment of impact or gunfire, but:

  • The shock wave from the bullet’s flight is separate from the impact noise or other subsonic sounds.
  • Once the bullet hits and stops, it no longer generates a Mach cone, but existing shock waves continue to travel, limited by the cone angle at the time of travel.

:repeat: The Mach Cone: Surface vs. Volume

  • The Mach cone is a 3D conical surface, not a filled-in volume.
  • The shock wave itself (which causes the sonic boom) is located on the surface of that cone — not throughout the interior.

:white_check_mark: So yes, when we say the boom is “heard inside the cone”, that’s misleading unless we specify:
:loud_sound: It’s heard when an observer is intersected by the Mach cone surface — not anywhere in the cone’s volume.

:brain: Why This Matters Physically

  • The shock front is a thin shell — a discontinuity — that moves outward and defines the cone.
  • Inside that cone (the volume), there’s no strong shock front. You might still hear residual sound (from the muzzle blast or impact), but not the shock wave from supersonic motion.
  • An observer hears the boom only when that conical surface sweeps over them — a very brief, sharply defined event.

:loud_sound: Sound After the Object Stops?

Also to reiterate from your original observation:

When the bullet (or object) stops, the Mach cone is no longer being generated, but the existing shock front (the cone surface) continues traveling at the speed of sound until it dissipates

:white_check_mark: Conclusion

You nailed it:

  • :x: The sonic boom isn’t heard inside the volume of the Mach cone.
  • :white_check_mark: It’s heard only when the surface of the cone passes over an observer.
  • :chart_with_downwards_trend: The boom is a product of the shock wavefront, which is geometrically the surface, not the interior.

This distinction is often glossed over in popular explanations, so it’s great you’re digging into it accurately. If you want, I can draw or simulate the geometry to show how this affects observers at different locations.

:dart: When the Supersonic Projectile Hits the Target:

At that instant:

  1. The projectile stops moving (or is destroyed).
  2. It no longer generates new shock waves, so no new Mach cone is formed from that point forward.
  3. But the existing shock wave — which was generated while it was moving — is still propagating outward.

:triangular_ruler: That Shock Wave Is Now a Truncated Cone

  • Think of the Mach cone as a conical shell expanding behind the moving projectile.
  • When the projectile stops at some point in space (say, position P), the Mach cone ends there.
  • What’s left is a truncated Mach cone (the front is “cut off” at P), and it continues to move radially outward at the speed of sound from all points along its surface.

:white_check_mark: Yes — this truncated cone-shaped wavefront continues to propagate outward, even though the source (the projectile) has stopped.

:boom: What Actually Happens to the Mach Cone

  • The Mach cone is a pressure wave: It’s formed by the bullet traveling faster than the speed of sound, compressing air molecules into a conical shock front trailing behind it.
  • When the bullet hits the target, it abruptly stops generating new shock waves. But the ones already emitted don’t just disappear—they continue propagating through the air.
  • The cone becomes truncated: Since no new waves are added, the cone no longer extends forward. What remains is a finite, expanding shell of pressure disturbances—like ripples after a stone hits water.
  • Energy dissipation: These shock waves gradually lose energy due to air resistance and dispersion. Eventually, they fade into ordinary sound waves and thermal energy.

You nailed it with “truncated conic surface.” That’s a much more accurate and physically meaningful description. Want to dive deeper into how shock waves behave in different media or how this compares to sonic booms from jets?

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