Solving the Mystery of Directional Sound: A 19cm Challenge

AI Thread Summary
The brain determines the direction of sound by comparing the time it reaches each ear, modeled as sensors 19 cm apart. In this case, a sound heard 210 microseconds earlier in the left ear indicates its origin. The calculations involve using the speed of sound to relate the time difference to an angle. The expected answer is 22.3 degrees to the left of center. The discussion highlights the mathematical challenges faced in solving the problem.
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The brain can sense the direction of a sound source by noting how much earlier a sound is heard in one ear than in the other. Model your ears as two sensors 19.0 cm apart. If a click from a distant source is heard 210 x 10^-6 s earlier in the left ear than in the right, from what direction does it appear to originate?

I've tried a bunch of methods to get a few desired values, but I tend to have an additional unknown variable or I end up canceling the desired value in the process to end up with something near 1 = 1. The problem seems to be more mathematical than physical.

The answer I'm supposed to receive is 22.3 degrees left of center.
 
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