Final answer:
The minimum distance a bat can detect with ultrasound echoes 1.00 ms apart is approximately 0.17 m, which in a multiple choice question rounds to the closest option 0.15 m. This may also explain why bats struggle to find an open door, as the door might be too narrow to be detected from a distance.
Step-by-step explanation:
To determine the minimum distance between objects that a bat can detect using ultrasound echoes 1.00 ms apart, we need to use the speed of sound in air. Assume that the average speed of sound in air is approximately 340 m/s. The bat sends out a sound and listens for the echo. When the echo returns in 1.00 ms, it has traveled the distance to the object and back again. Therefore, to find the minimum distance to the object, we divide the total distance traveled by sound by 2.
The total distance traveled by sound in 1.00 ms (which is 0.001 seconds) is:
Distance = Speed × Time
= 340 m/s × 0.001 s
= 0.34 m
To find the one-way distance, we divide by 2:
One-way Distance = 0.34 m / 2
= 0.17 m
This value is slightly larger than 0.15 m and smaller than 0.30 m, so the minimum distance that the bat can detect objects is approximately 0.17 m. For multiple choice questions, the closest answer would be 0.15 m (option a).
Regarding question (b), this minimum distance can indeed explain the difficulty bats may have in finding an open door. If the door's width is smaller than twice this distance, the bat might not detect it as a passage until it is very close.