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## Speed of sound and sound detection lag between ears

1. The problem statement, all variables and given/known data

One cue your hearing system uses to localize a sound (i.e., to tell where a sound is coming from) is the slight difference in the arrival times of the sound at your ears. Your ears are spaced approximately 20 cm apart. Consider a sound source 5.0 m from the center of your head along a line 45 degrees to your right.

What is the difference in arrival times? Give your answer in microseconds.

2. Relevant equations

v=d/t
speed of sound in air @ rm temp = 343m/s

3. The attempt at a solution

I set up the problem as so:

http://photo.ringo.com/230/230995202O179609724.jpg

http://photo.ringo.com/230/230995202O179609724.jpg

and then calculated the two dark red lines as different hypotenuses of the two different triangles (one is L+0.1 and the other is L-0.1), then I used v=d/t (with some manipulations) and got a difference which was incorrect

then i tried to set it up as 5 being the main hypotenuse (dashed turquoise), and did a similar process, again wrong

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