Sound triangulation using cheap microphones

Sound triangulation is a method of determining where a sound originated from. Triangulation can give the location of a sound source in 2-d space. A sound wave travels out from its point of origin as a sphere. Trilateration is another method a locating the source of a sound. It is modeled around the fact that sound waves travel out spherically. See the below images for a better description of what I mean.

diagram describing trilateration

Trilateration

Picture source : http://en.wikipedia.org/wiki/Trilateration

It had very useful military applications:

artillery

artillery

Picture source : http://en.wikipedia.org/wiki/Sound_ranging

The equations for the Trilateration model of sound location were a bit difficult for me to understand well enough to build a project around them. Triangulation solves this problem by using a much simpler model of sound location. It assumes that all sound waves from a sound source travel out in a planer way(straight lines) instead of in a spherical way. This greatly simplifies the equation to a few variables that are related by basic trigonometry.

picture demonstarating planar sound waves

planer sound diagram

The equation is simplified to :

\Delta t = \frac{x sin{\theta}}{c}

where:
\Delta t is the time difference in seconds
x is the distance between the microphones in meters
\theta is the angle between the baseline of the microphones and the incident sound, in degrees
c is the speed of sound

This blog is incomplete, will add in project details later.

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