Question

A hunter is standing on flat ground between two vertical cliffs that are directly opposite one another. He is closer to one cliff than the other. He fires a gun and, after a while, hears three echoes. The second echo arrives 1.76 s after the first, and the third echo arrives 1.38 s after the second. Assuming that the speed of sound is 343 m/s and that there are no reflections of sound from the ground, find the distance (in m) between the cliffs?

Answer 1

person between two vertical cliffs and closer to one cliff than the other.
let x = distance from person to closer cliff
let y = distance from person to more distant cliff
343 m/s = speed of sound

1st echo comes from closer cliff and travels 2x to person's ear
2nd echo comes from more distant cliff and travels 2y to person's ear
time separation between 1st & 2nd echo = 1.76 s
distance/speed = time = 1.76s = (2y - 2x)/343
2(y-x) = 343(1.76) = 603.68
y-x = 301.84m

3rd echo comes from 2nd echo sound after it reverberates
from closer cliff to person's ear. Time separation between 2nd & 3rd
echo = 1.38 = 2x/343
2x = (343)(1.38) = 473.34
x = 236.67 m
y = 301.84 + 236.67 = 538.51 m
distance between cliffs = x+y = 236.67 + 538.51 = = 775.18 m ANS