So. Tonight's episode involved using a "Sine Wave Generator Program" which created a waveform that was turned into an MP3, which was subsequently played back with an iPod attached to a battery powered set of speakers. This waveform simultaneously set up sympathetic vibrations in all the glass cases inside the jewelry store. The CSIs were able to track down the distributor of the Sine Wave Generator Program, and track the purchase to a P.O. Box.
There are so many things wrong with this:
- Sine Wave Generator Program - the criminals involved were college students, it seems likely to me that if they understood enough about sympathetic resonance to conceive of a scheme to shatter glass, they'd be capable of writing a program themselves to generate a sine wave. To prove that it could be done by a hobbyist, I wrote a 30 line program to generate sine wave WAV files. The whole idea of using sound was to eliminate evidence at the scene - why buy a commercial sine wave program (with the associated paper trail) when you can write your own? And, if you're lazy, you can download a free one.
- audible to dogs, inaudible to humans - Humans can hear in a range from 20 cycles per second (hertz) to around 20,000 hertz. Unless, like me, you've listened to a little too much Phil Collins on the Walkman back in your youth, in which case you can't hear that full range. Dogs can hear about one octave up from us, a range from 40 hertz to 46000 hertz. This means that the glass-breaking sound would have to be in a band between 20,000 and 46,000 hertz.
There are several problems here. For one thing, somehow they discerned that the theives were using MP3 as their file format, instead of WAV, AIFF, AAC, or whatever else. MP3 is familiar, but wouldn't have been used for a couple of reasons. First, it's a lossy format, which means that you'd get degradation of your pure waveform, which isn't what you want. Secondly, MP3 is designed for human listeners - if you try to MP3 encode a signal outside the range of human hearing, you'll get silence. Not just "inaudible signal" - a total lack of signal. This is actually a feature, MP3 throws away stuff that you don't want to listen to and passes the savings on to you in the form of a smaller file.
- what's the resonant frequency of a display case, anyway? - here's an exercise you can do at home. Take a wine glass, or a fish bowl, or a plate glass window. Flick it with your fingernail. The better the quality of the crystalline structure involved, the clearer the ringing sound will be. Ideally, you'd get a pure tone, a single frequency. But one thing that I'm pretty sure you'd get would be an audible frequency. The smaller the glass, or the higher the tension on the glass, the higher the frequency. But maybe you just rang a wine glass, and maybe it was around 600 hertz. The display cases pictured were much larger than your wine glass, so their ringing frequency would have been substantially lower than your wine glass. And, as I mentioned above, the range where a dog can hear something and a human can't is up in the higher ranges, so a low note isn't helping us.
Also, consider that every display case in the store seemed to shatter simultaneously. If you were putting out a pure tone, the shapes of all the panes of glass would have to be the same to get the same ringing frequency. If you weren't putting out a pure tone, if you were using a shotgun approach to cover multiple frequencies at once, you'd have a much harder time getting the glass to resonate with your signal, because you're splitting your power up amongst the different frequencies.
So, assuming that all the display cases had the same resonant frequency, how do you find the frequency? Mythbusters did a segment where they had a piece of hardware that generated pure sine wave tones, and it took quite a bit of work to find the right frequency, and once they found it, they had to spend several seconds at that frequency for the vibrations to break glass.
- "Moon River" - yeah, it was cute that their MP3 of an inaudible tone had been titled the same thing as the song from "Breakfast at Tiffany's", but there's no reason you'd need to have a song-length file - three minutes of inaudible tone is certainly overkill.
As an experiment, I wrote this program to prove that generating sine waves is something that amateurs can do with no special training. The output of it is this WAV file, which I proceeded to encode into this MP3 file. WARNING - the audio files have pure tones, and I insist that you not listen to them with headphones. If you want to listen to them on speakers, you might want to turn the volume down before playing them. That said, go ahead and play them - the files are each 16 seconds long, starting at 343.75 cycles per second and stepping up an octave every two seconds. This means that 12 seconds into the playback, the signal is 22,000 cycles per second, a sound that you can't hear, but a dog can. At 14 seconds into playback, the frequency is 44,000 cycles per second, which is getting up to the point where signal reconstruction is problematic (indeed, the WAV file isn't able to reproduce 44,000 cycles per second correctly, and the MP3 doesn't even try).
Did you play the MP3 file? Did glass break? I didn't think so.