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 y " from " H_2` as shown in figure. The time interval between the original sound and echoes from `H_1 and H_2` will be respectively.

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 times `t_1` while II echo from `H_2` after time `t_2`, III echo will be produced due to reflection of sound of I echo from `H_2` or of II echo from `H_1`, i.e., `t_3 =t_1 +t_2 =1.5 +2.5 = 4 sec`i.e., III echo will be produced after 4 sec. and in it sound from both I and II echoes will reach simultaneously.