David Morgan's Fourier Series assignment

I have a strong interest in guns and shooting. One application for a fourier series that relates to guns would be to use fourier series to map out the sound signature of a gunshot. Once this is done, then it would be possible to invert that fourier series, and then run that signal out to a speaker. When played alone, this would sound just like the original gunshot, but if it was timed right and played in synchronization with the original gun shot when the gun is fired, the wafe form of the gunshot and the wave form of the fourier series inverted wave form would interact and create destructive interference. This will result in canceling the sound signature of the gunshot. This would have many practical applications, such as eliminating the need for hearing protection when shooting, reducing hearing loss from shooting, and tactical applications where sound suppressors are currently used.

I don't have the equipment to record a gunshot of my own and then extract an equation for the sound wave. I looked online for one, but I couldn't find what I was looking for. I found a couple recordings of gunshots, but I couldn't figure out how to find an equation for the sound wave, because all I could find was jpeg images of a wave form.

If I could have found what I was looking for, I could have found the fourier series for the equation of the sound wave for a gunshot. I could then just shift my timing of my replicated sound over by half a period. Since sound waves are periodic and follow the form of sin and cosine waves, shifting the wave over half a period and then ovelaying it with the original wave would cause destructive interference and result in no net sound. Thus the sound of the gunshot would be eliminated.

My dilema is that I don't have the equipment to gather the data and test my theory. One major obstacle in actually performing this project would be devising a meathod to time my replicated gun shot sound to the gun firing so that the waves overlap at the right time and actually interact destructively. If the timing is off by just a smudge, the waves will interfer constructively and cause an even louder gun shot, or sound like two separate shots being fired.

So this is one possible application of a fourier series that is related to one of my interests.

David Morgan Oct 31, 2010