As some here are aware, there is a large and interesting literature that
grapples with the problems of passively locating animal vocalizations (rather
than impulse noises) with microphone /hydrophone arrays. There are issues
about multipath transmission and the challenging problem of deciding which
among similar somewhat degraded acoustic events received at each
microphone is the same event so you can apply the math Steve has outlined.
There are remarkable findings including inferences that terrestrial animals
from insect ot elephants call at particular times of day because the
atmospheric conditions greatly enhance transmission distances.
Bernie has had a lot to say in this arena.
For folks conversant with the math (Monte Carlo methods) a recent paper
might be worth a look:
Spiesberger, J. L. 2005. Probability distributions for locations of calling
animals, receivers, sound speeds, winds, and data from travel time
differences. Journal of the Acoustical Society of America 118:1790-1800.
Bill R.
>
> Rich:
>
> I live in a city so I hear lots of hand guns too. But I'm always pretty
> sure where
> the shots are coming from: the 24 hour store on the corner.
>
> Here's back-of-the envelop stuff to see if we're close enough to what
> you could do to make more calculation
> worth it. The basic geometry is sketched in
> (http://math.uc.edu/~pelikan/Dora/Instructions.html)
>
> A formula for finding a bearing theta to a distant object based on time
> of arrival of sounds at two microphones is
>
> theta = arcsin( V dt/D) here V=speed of sound, D is distance between
> mics and dt is difference in time of arrival.
>
> To locate something to within 100 feet at a mile means getting the angle
> right to a couple degrees.
>
> This boils down to (assuming middling values of theta and V=333 m/sec)
>
> D = (333/0.02) X
>
> where X is how accurately the time of arrival difference can be
> measured. With values between 0.001 sec (generally easy to do) and
> 1/(22050) (very tricky to do with 44.1KHz sampling) this gives D in the
> range 1 -17 meters. How well you can "align" the tracks pretty much
> determines X --- gunshots should be pretty easy, but ambient noise (like
> wind) makes things harder.
>
> With 3 microphones the baselines for the pairs are all oriented
> differently and usually one pair has an unfortunate value of theta. So
> probably you'd be looking at trying to put mics at the corners of an
> equilateral triangle with side length on the order of 30 feet or so.
>
> Don't start hauling cable! But if this is close to doable, let me know
> and I'll get out a calculator.
>
>
> Thanks,
>
> Steve P
>
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