Final answer:
Using the distance traveled by sound and the time taken for the echolocation pulse to be received back, the bat's speed is calculated to be approximately 14.14 meters per second.
Step-by-step explanation:
Calculating the Bat's Speed
To calculate a bat's speed using echolocation, we must first determine the speed of sound at the given air temperature. At 20°C, the speed of sound in air is approximately 343 meters per second. The bat emits a sound pulse that has to travel to the wall and back, covering twice the distance to the wall. The total time for this round trip is 0.28 seconds.
The distance to the wall is given as 50 meters, so the sound has to travel 50 meters to the wall and 50 meters back, for a total of 100 meters. Since time is given for the round trip (there and back), we use the formula distance = speed × time to find the total distance traveled by the sound.
Thus:
- Speed of sound = 343 m/s
- Total distance traveled by the sound = 100 m
- Total time = 0.28 s
Using the formula:
343 m/s = Total distance traveled / Total time
Total distance traveled = 343 m/s × 0.28 s = 96.04 m
Since the total distance traveled by sound is twice the distance to the wall, the bat must be moving towards the wall for the actual traveled distance to be short of 100 meters (the expected distance if the bat were stationary). The difference between the actual distance (96.04 m) and the expected distance (100 m) is the distance covered by the bat in the given time.
The bat's distance covered = 100 m - 96.04 m = 3.96 m
Now, we can calculate the bat's speed:
Bat's speed = Bat's distance covered / Total time
Bat's speed = 3.96 m / 0.28 s ≈ 14.14 m/s
Therefore, the bat's speed is approximately 14.14 meters per second.