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
speed of sound in air @ rm temp = 343m/s
3. The attempt at a solution
I set up the problem as so:
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