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 1.15 s after the first, and the third echo arrives 0.653 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

at t1 first echo arrives and t1 is unknown
t2 is heard 1.15 s after the the firstecho, or t1. So, t2 =1.15 s + t1
t3 is heard 0.653 s after the second echo, meaning that itstarted from the person's ear, traveled 0.653 s and was heard again.Therefore, t1 and t3 are the same since theyboth started from the person and returned before going anywhereelse.

now using formula

t1 = 2x1/343

and t2 = 2x2/343

since t1 = t3, so t1 = 0.653 sec

x1 = 0.653*343/2 = 112 m

t2 = 1.15 + t1 = 1.803 sec

x2 = 1.803*343/2 = 309.2 m

distance between the cliffs = 112 + 309.2 = 421.2 m