Eric Hufschmid on the now fugitive Chris Bollyn

http://www.erichufschmid.net/TFC/Bollyn-Broken.html

Arthur

Because I have a real job, and a real life outside of this forum, and I didn't feel like wading through 100pages of this cr@p to find it. I figured that if you cared so much about it, you could wade through it yourself. Be my guest.

That blast waveform that Trippy provided that you did the attack/decay bit on was stretched-out not only by the dispersion of the atmosphere, but by multiple reflections from the ground (if it was recorded as he described it). That doesn't contradict what I've been saying, it supports it. That's the "echoes of echoes" effect, where a reflection takes a slightly longer geometric path which takes a slightly longer propagation time, and so arrives slightly later than the components that took slightly more direct paths.

The "3.3milliseconds" number at 48 feet likewise showed the effect of the echoes-of-echoes off the surrounding environment. It wasn't a "pristine" recording of just the detonation propagating through free-space, which could (if no other blunders were made) provide an actual recording of the blast-pressure-versus-time plot (i.e., characteristic sound of an explosion), but I'm gratified that the plot at least showed the rise-time as a vertical line, something you've already said was impossible. A good recording of what the explosive itself would sound like would require that the explosive have nothing else in the environment for the explosion to reflect off of, at least during the interval of interest.

All they'd have had to do would've been to suspend the explosive from a long line so that it isn't near anything else and record the sound with a microphone with bandwidth capability at or at least near 1MHz, so as to get a better idea of what that leading edge looks like. (It isn't vertical in the real world. In the recording, that's an artifact of undersampling, one sample is before the detonation happens, the next collects the average value of the complete detonation, and the next sample, the explosion is already over and all you're measuring is the hot gas passing your mike by at the speed of sound.)

In your library of sound books, you should have *some* reference that discusses the bandwidth of signals and what happens when the recording equipment has insufficient bandwidth to capture a signal with greater bandwidth. A "spike", or impulse, has energy in all spectral components (just like white noise). A C-4 detonation is a good approximation, and that's all that's possible in the real world, an approximation. An idealized spike contains all possible frequencies, including GHz, for instance, but C-4 has less bandwidth than an ideal spike, which is related to the rise-time of the blast. You can get a good first-cut estimate of a spike's peak bandwidth by looking at the steepest slope in the signal and taking 1/x of that. A one-microsecond rise time would correspond (roughly) to a 1MHz signal bandwidth. A 40kHz sampling rate will lose all the information content of the spectrum of a 1MHz signal between 20kHz and 1MHz. That's most of the explosive's "characteristic" sound energy, lost due to undersampling.

It should also be noted that explosives have a "DC" component to their spectrum, and we can't hear that, either (nor do microphones record that). So any recording of an explosion made with a microphone will have artifacts at both ends of the spectrum.

That's the reason DARPA put out an SBIR RFP for the development of a sensor capable of capturing the acoustic characteristics of explosives several years back. (I considered bidding on that one, myself.) I was going to post a link to the DARPA program, but google let me down.