Question

A boy shouts inside a deep well and hears the echo $0.4s$after shouting. If the speed of sound is $340m/s$find the depth of water level as well.
A. $78m$
B. $88m$
C. $68m$
D. $58m$

Answer 1

As we know echo is the concept of reflection of sound wave from a distant obstacle and path covered by it can be whether straight or curved so we can directly use $d = v \times t$ where is $d$ distance, $v$ is speed and $t$ is time.

Complete step-by-step solution:
In the given question let $d$ be the distance of the boy from water level as well, therefore the total distance covered by sound waves will be double of the distance we have assumed $2d$.
Speed of sound as given, $v = 340m/s$
Time as given in question, $t = 0.4s$
As sound wave has to cover double distance as we have assumed so we time taken to cover each side of the distance will be half of the total time so time will become $\dfrac{t}{2}$ and value will become $0.2s$
Therefore, $d = v \times t$
$d = 340 \times 0.2$
$d = 68m$
Therefore the correct option is C.

Note:- We know the speed of sound is $340m/s$ and it has to travel double distance to go to an obstacle and traverse back path so we have taken the half time as we did in the solution of question. So we can use the normal equation $2d = v \times t$ where distance is double due to double path and here we will take total time as per given in the question. The sonar device sends out a sound and automatically calculates the distance, sonar uses sound waves while radar uses electromagnetic waves. This method is also used by dolphins to save themselves from being hit by obstacles in sea and also in medical sciences and also in some types of submarines. And the average speed of sound is $343m/s$.