Question

A person is in between two vertical mountains. The person fires a gun then hears the first echo from the nearby mountain in a time 3s and hears second echo from far mountain in a time 4s. The person hears the third echo after

• A. 5 s
• B. 6 s
• C. 7 s
• D. 8 s

Answer 1

The correct option is C 7 s

Distance travelled by sound waves for echo:
$2x=$ speed of sound $\times$ time of echo
$x=\frac{{\vartheta }_s\times 3}{2}$ -------(1)

Distance travelled by sound waves for echo 2:
$2(d-x)=$ speed of sound $\times$ time of echo 2
$2d-2x={\vartheta }_s\times 4$ ------(2)

Now putting value of $2x$ from (1) in (2)
$2d-{\vartheta }_s\times 3={\vartheta }_s\times 4$
$2d=7{\vartheta }_s$

Distance travelled by sound wave for echo 3
$2d={\vartheta }_s\times$ (time of echo 3)
$\frac{2d}{{\vartheta }_s}=$ time of echo 3

From (3): $\frac{2d}{{\vartheta }_s}=7$

So, time of third echo is $7$ seconds.