Question

A bat chasing a moth emits a sequence of three chirps every 0.010 seconds and later hears the echos of the chirps as detailed in the diagram shown. Question: How far away is the moth when the bat hears the third echo? Make sure to explain how you arrived with your answer.

Answer 1

First, take into account that the difference in time between the third chirp and the third echo is:

t = 0.10s - 0.02s = 0.08s

next, consider that in such a time, the sound emitted by the bat travels twice the distance in between the bat and the moth, then, you have:

2d = v*t

where v is the speed of sound 340 m/s

solve the equation above for d, and replace the values of the previous parameters, as follow:

d = v*t/2

d = (340 m/s)(0.08 s)/2

d = 13.6 m

Hence, the distance between the moth and the bath is 13.6 m