A hunter is standing on flat ground between two vertical cliffs that are directly opposite one another. He is closer to one cliff than to the other. He fires a gun and, after a while, hears three echoes. The second echo arrives 1.6 s after the first, and the third echo arrives 1.1 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 between the cliffs.?

652 m

Explanation:

Let the distance between the hunter and the closer cliff be d1 and the distance from the hunter to the further cliff be d2.

Let t1 be the time taken by first echo after travelling distance d1 and return to hunter  

 t1=2d1/343      where 343 is speed of sound in air.

Similarly let t2 be the time taken by second echo after travelling distance d2 and return to hunter  

t2=2d2/343

The second echo arrives 1.6 second after first and hence  

t2-  t1=1.6

2d2/343-2d1/343=1.6

d2-d1=274.4

Let t3 be the time taken by third echo, which arises from sound of second echo which is reflected from closer cliff.  

t3=2d1/343

d1=189 m                                               given t3=1.1 sec

The equation first becomes as  

d2-189=274.4

        =463 m

thus the distance between cliff is determined as

d1+d2=189+463

         =652 m