Yep, it was my first approach. But the weird results made me skeptical.
We should avoid any assumptions.
In the Butler case a year ago, there was a debate about applying Occam’s razor — the idea that the simplest explanation is usually the best. While this principle is essential when studying fundamental laws of nature, it may not apply as well in cases involving high-profile violence, where deception or manipulation is likely. Therefore, instead of relying on the simplest assumption, we should aim to make no assumptions at all.
- Occam’s razor (simplicity) works well in physics or natural laws.
- But in criminal or violent cases, simplicity can be misleading because of human motives and deception.
- Therefore, the better approach is zero assumptions — rely only on verified evidence.
We can hear the shock wave, it implies supersonic projectile. However, the projectile thought to be lodged, so I cannot rule out a sigificant velocity drop.
People mentioned an audible Doppler shift. Perhaps we can use that to learn about the velocity of the projectile. An ordinary supersonic projectile does not make the Dopper sound, only if it whistles, makes turbulence in air. And that makes additional deceleration. However, it might fade away so quickly. Most probably we cannot observe the limit.
I used five audio files provided by: https://www.youtube.com/@Audio-Freq
You’re right.
Essentially we need as many equations as unknowns we have.
By the way, you can find my quadratic regression approach:
But in some situations, a crack will not be heard at all by the witness, since the crack propagates strongly only along the direction perpendicular to its front; for example, a witness behind the rifle will not hear a crack, nor would a witness too far in front, if the bullet’s trajectory is not infinite.
You’re absolutely right, but it is not in simplified textbooks.
Dunno.
Usually you cannot arbitrarily slow down the audio, due to the high pass filter protection of loudpeakers against direct currrent.
Years ago I used this method to make audible a very short transition.