A person standing between two parallel cliffs fires a gun and hears two echoes, first echo after 1 second and second echo after 3 second. The distance between the two cliffs is (The velocity of sound = 330 m/s)

Step-by-step solution

Let the distance of the person from the first cliff be d₁ and from the second cliff be d₂ . The time taken to hear the first echo is t₁ = 1 s. The sound travels to the first cliff and back, so the distance covered is 2d₁ . 2d₁ = v t₁ 2d₁ = 330 1 = 330 m d₁ = 165 m The time taken to hear the second echo is t₂ = 3 s. The sound travels to the second cliff and back, so the distance covered is 2d₂ . 2d₂ = v t₂ 2d₂ = 330 3 = 990 m d₂ = 495 m The total distance between the two cliffs is d = d₁ + d₂ . d = 165 + 495 = 660 m