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A man stands at a distance of \[250m\] from a wall. He shoots a rifle and hears the echo after $1.5s$ . Calculate the velocity of the sound.
A) $333m{s^{ - 1}}$
B) $383m{s^{ - 1}}$
C) $433m{s^{ - 1}}$
D) $483m{s^{ - 1}}$

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Last updated date: 20th Jun 2024
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Answer
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Hint: An echo is the bouncing back of sound after the sound wave hits on a hard surface like wall or cliff, valley or canyon. We use the simple distance velocity and time relation to find the answer to this problem.

Complete step by step solution:
When the sound wave leaves the source, it vibrates the air around it and travels ahead and when it reaches a hard surface then it bounced back from there causing an echo. The echo cannot be formed if there is no reflecting surface or the source is far away from the reflecting surface.
Echo is formed only under certain conditions being fulfilled. The conditions for an echo are:
The distance between the source of the sound and the reflected surface should be equal to or more than $17meters$ and the time between hearing of the original sound and that of the echo should be more than $0.1s$ .

Here in this question it is given that the distance between the man and the wall is \[250m\] and the time after which the echo is heard is $1.5s$ , thus satisfying the conditions for an echo.
Let us consider,
The distance between the man and the wall be $d = 250m$
Time after the echo is heard is $t = 1.5s$
For the echo to occur, the sound wave travels a distance of $2d$ as the distance from the rifle to wall and then bouncing back from wall to man.
Using this given data we can find the velocity by the speed-distance-time formula as
$v = \dfrac{{2d}}{t}$ ( $\because $ sound travels a distance of $2d$ )
$\therefore v = \dfrac{{2 \times 250}}{{1.5}}$
$ \Rightarrow v = \dfrac{{500}}{{1.5}}$
$ \Rightarrow v = 333.33m{s^{ - 1}}$

Therefore, option (A), $333m{s^{ - 1}}$ is the correct answer.

Note: Make sure that all the quantities are in their SI units or in the same units during calculations to get the correct answer. There are three different categories under which sound waves can be classified, namely longitudinal waves, mechanical waves and pressure waves.