Re: The mathematics of Triangulation

From: sbben (sbben_at_comcast.net)
Date: 08/29/04 

Date: 29 Aug 2004 15:24:27 -0700

panoptes@iquest.net (Daniel W. Johnson) wrote in message

> For the sake of definiteness, let's say the distance between receivers 1
> and 2 is long enough for sound to take 6 seconds to travel from one to
> the other. With the units as sound-seconds, this puts the x,y
> coordinates of the receivers at (-3,0), (3,0), and (0,-6), respectively.
>
> If the gunshot is at (0,3), receivers 1 and 2 will detect the sound 4.24
> seconds (NOT 3) after the shot and receiver 3 will detect it 9 seconds
> after the shot, for a difference of 4.76 seconds. If the gunshot is at
> (0,6), receivers 1 and 2 will detect the sound 6.71 seconds (NOT 6)
> after the shot and receiver 3 will detect it 12 seconds after the shot,
> for a difference of 5.29 seconds.

Ok, I think I get it. Will the difference in delay be due to the arc
of the sound wave?

Situation 1 (the "." is the source)

   | . | 4.76 second delay
    \ _ /

Situation 2
      
| . | 5.29 second delay
 \ /
   -- _ --

In the second situation the arc is greater (since the circle has
expanded) and therefor the delay is greater for the third reciever
like you said right?

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