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 1.27 s after the first, and the third echo arrives 0.642 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

Let total distance between the cliffs =L

distance of nearer cliff = d

distance of farther cliff = L -d

Velocity of sound = v =343 m/s

time after which first echo arrives = t₁ =2d /v

second echo arrives after reflection from farther cliff,

for second echo sound traveled distance=2 (L-d)

time after which second echo arrives = t₂ = 2(L- d ) /v

The second echo arrives 1.27 s after the first

therefore time interval between first and second echo=2(L-d)/v - 2d/v = 2( L -2d) / v

time interval between first and second echo= 2(L -2d ) / v =1.27 s

2(L -2d ) / v =1.27 s

third echo is produced by sound which traveled from hunter gun to farther cliff and then to nearercliff and after these two reflections the sound reaches the hunter

for third echo sound traveled distance=[ (L-d) + L +d ] =2L

the third echo arrives 0.642 s after the second.

time interval between second and third echo = 2d /v

2d / v = 0.642

d =0.321 v = 0.321*343=110.103 m

2(L -2d ) / v =1.27

2(L -2*110.103 ) / v =1.27

L - 220.206 = 217.805

L = 438.011 m

the distance between the cliffs is 438.011 m and hunter is 110.103 m from the nearer cliff and 327.908 m from the farther cliff