Question

The speed of sound through air at room temperature and standard pressure is about 343 m/s. One cue the human hearing system uses to localize sound is the slight difference in the arrival times at the two ears of the sound emanating from a source. Ears are spaced about 20cm apart. Consider a person facing the positive x-direction and a source located 5 m away at an angle of 45° below the positive x-direction. What is the difference in arrival times of sound from this source arriving at the persons two ears. Give an answer in µs.

Answer 1

77GM The sm di y E2 - 7 Sound source

v=343 m/s, a =5m, g = 45°, D = 20cm . R = 10 cm = 0.im ! di= d x² + (y+R) 2 Ic= a caso and y= d sine is dia 1 (dcos e) + (d sin e+R) 2 dia J (5 cos 45)² + (5 sin45 t 0.1)? di â 5.0712 m o idu Now d2 = x² + Ly-R2 do = ld cos 0) ² + (asino -R) ² de V (5 Los 45) ²+ (5 sin 45-0.1² daa 4.9298m

Ad=di-d₂ = 5:0712-4.9298 od = 0.1414 m At = Ad = 0.1414 = 4.1810-4 seconds - 343 su us at = 410 us Answer