Question

A man standing between two cliffs hears the first echo of a sound after $2$ seconds and the second echo $2$ seconds after the initial sound. If the speed of sound be $330m{s}^{-1}$, the distance between the two cliffs should be

• A. $1650m$
• B. $990m$
• C. $825m$
• D. $660m$

Answer 1

Answer: (D)

$660m$

If the man plays a sound, then the sound waves travel towards the cliff, get reflected, return and then fall on his ear. This is how he hears an echo.

Thus the sound travels twice the distance between him and the cliff.

$\therefore distance\left(s\right)=\frac{speed\times time}{2}$

$\therefore s=\frac{330\times 2}{2}=330$ metres

Thus 330 metres is the distance between him and the 1st cliff.

Since he hears the 2nd echo after the same time interval, the 2nd cliff is also at a distance of 330 metres from him.

Hence the distance between the 2 cliffs will be $330+330=660m$.