A person standing between two parallel hills fires a gun. He hears the first echo after `(3) /(2)` s, and a second echo after `(5) /(2)` s. If speed of sound is `332 m//s` , Calculate the distance between the hills. When will he hear the third echo?

Explanation

Let the person P be at a distance x from hill `H_(1)` and from `H_(2)` as shown in figure-6.6. The time interval between the original sound and echoes from`H_(1)` and `H_(2)` will be respectively
`t_(1) = (2x)/(v)` and `t_(2) = (2y)/(v)`

So the distance between the hills,
`x + y = (v)/(2) [t_(1) + t_(2)] = (332)/(2) [1.5 + 2.5] = 664 m`
Now as I echo will be from `H_(1)` after time `t_(1)` while II echo from `H_(2)`after time `t_(2)` III echowill beproduceddue to reflectionof soundofI echo from `H_(2)` or ofII echo from `H_(1)` thus we have
`t_(3) = t_(1) + t_(2) - 1.5 + 2.5 = 4s`
Thus we can state that III echo will be produced after 4s and init sound from both I and II echoes will reach simultaneously.