Question

A sound signal is sent in air and water both simultaneously from a boat on a rover.The echo of sound strike by river bed is heard in $4\sec $ , while echo strike by aeroplane is heard in $8\sec $. Find the distance between aeroplane and river bed.
$[$Velocity of sound in air $ = 350\,m\,{\sec ^{ - 1}}$ velocity of sound in water $ = 1500\,m\,{\sec ^{ - 1}}]$
A. $4.4\,km$
B. $6.4\,km$
C. $8.8\,km$
D. $13.4\,km$

Answer 1

Hint:In order to solve given question, we need to find distance travel by sound in both water and air with their respective velocities and time taken to come back after reflection from river bed and aeroplane and then add these two distances to get final distance between river bed and aeroplane.

Complete step by step answer:
Let us first find the distance traveled by sound in the river bed from time to signal sent and received. Since, we also know Time taken for an echo to heard is twice the time taken to travel the distance so, distance travelled by sound in water is ${S_{Water}}$ in the time $t = 2\sec $ which is given as,
Velocity of sound in water $ = 1500\,m\,{\sec ^{ - 1}}$
${S_{Water}} = 2 \times 1500$
$\Rightarrow {S_{Water}} = 3km \to (i)$
Now, we will find distance travel by sound in air is given as
Velocity of sound in air $ = 350\,m\,{\sec ^{ - 1}}$ and time taken to cover distance is $t = 4\sec $.
${S_{Air}} = 350 \times 4$
$\Rightarrow {S_{Air}} = 1.4\,km \to (ii)$
From equations $(i)\,and\,(ii)$ we get,
Distance between river bed and aeroplane is $ = 1.4 + 3$
Distance between river bed and aeroplane is $ = 4.4\,km$

Hence, the correct option is A.

Note: Remember, an echo sound is formed when a sound wave gets reflected on a surface gets heard back to the listener and in this total time taken to form an echo it just doubles the time taken by a sound wave to travel the actual distance between surface of reflection and listener.