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 1.97 s after the first, and the third echo arrives 1.00 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

The answer is actually much simpler.



t₁ is unknown
t₂ is heard 1.97 s after the the firstecho, or t₁. So, t₂ =1.97 s + t₁
t₃ is heard 1.0 s after the second echo, meaning that itstarted from the person's ear, traveled 1 s and was heard again.

Therefore, t₁ and t₃ are the same since theyboth started from the person and returned before going anywhereelse.

Use the followingequations:



Since t₁ =t₃, t₁ = 1 s

1 = 2(x₁) / 343

x₁  = 171.5 m

Since t₂ = 1.97 s + t₁,

t₂ = 2.97 s

2.97 = 2(x₂) / 343

x₂ = 509.3 m

simply add them together.

You should get 171.5 m + 509.3 m = 680.8 m (answer) it is tthe distance between the cliffs