Answer:
a) t_l - t_r = 12.54 us
b) (t_l - t_r) / T = 0.0157
Explanation:
Given:
- Frequency of source f = 1250 Hz
- Distance from source to right ear d_r = 2.6 m
- Distance from source to left ear d_l = ?
- Separation between ears s = 0.15 m
Find:
a. What is the difference in the arrival time of the sound at the left ear and the right ear?
b. What is the ratio of this time difference to the period of the sound wave?
Solution:
- Apply Pythagoras theorem to calculate the distance d_l from source to left ear:
d_l = sqrt ( 2.6^2 + 0.15^2)
d_l = sqrt ( 6.7825 )
d_l = 2.6043 m
- The time deference can be calculated from a simple distance - speed formula:
t_l - t_r = (1 / v) * ( d_l - d_r)
Where, v = 343 m/s speed of sound in air:
t_l - t_r = (1 / 343) * ( 2.6043 - 2.6)
t_l - t_r = ( 0.0043 / 343 )
t_l - t_r = 12.54 us
- Now we compute the Time period of the sound wave:
T = 1 / f
T = 1 / 1250 = 8*10^-4 s
- The ratio of differential time to Time period T is:
(t_l - t_r) / T = 12.54 * 10^-6 / 8*10^-4
(t_l - t_r) / T = 0.0157
