A bat flying in a cave emits a sound and receives its echo
0.1 s later. Show that the distance to the wall of the cave
is 17 m.
To find the distance to the wall of the cave, we need to use the formula:
Distance = Speed × Time
In this case, the time is given as 0.1 seconds. But we still need to determine the speed of sound.
The speed of sound in air is approximately 343 meters per second at 20°C. However, this speed can vary depending on factors such as temperature and humidity.
Now, to find the distance, we need to split the total time into two parts: the time taken for the sound to reach the wall and the time taken for the echo to return.
Given that the total time is 0.1 seconds, we can assume that the time taken for the sound to reach the wall is half of this time, which is 0.1 seconds divided by 2, resulting in 0.05 seconds.
Using the formula, we can calculate the distance:
Distance = Speed × Time
Distance = Speed × (0.1 / 2)
Now, substituting the speed of sound (343 m/s) and the time taken for the sound to reach the wall (0.05 seconds):
Distance = 343 m/s × 0.05 s
Distance = 17.15 meters
Therefore, the distance to the wall of the cave is approximately 17 meters, given the assumptions we made about the speed of sound and the time taken for the sound wave to reach the wall.