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A boy dropped a stone in a $45 m$ deep well. After how much time will he hear the splash if the speed of the sound is $340 m / s$ ? Take $g = 10 m s^{- 2}$

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3.11 s

3.12 s

3.13 s

3.14 s

answer is C.

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Detailed Solution

If the speed of sound is

340 m / s

, the boy will hear the splash after

3.13 s

.
An echo is a reflected sound that is produced after reflecting back from an obstacle.
Given,
Depth of the well is given,

h = 45 m

, speed of sound,

v = 340 m s^{- 1}

and

g = 10 m s^{- 2}

Time after which splash can be heard (

T

)

=

Time taken by stone to reach the water surface (

t_{1}

) + time taken by splash sound to reach the boy (

t_{2}

)
As the stone is under free fall, hence,

s = ut + \frac{1}{2} a t^{2}

So,

h = 0 + \frac{1}{2} {gt 1}^{2}

\Rightarrow t_{1} = \sqrt{\frac{2 h}{g}}

\Rightarrow t_{1} = \sqrt{2 \times \frac{45}{10}}

\Rightarrow t_{1} = 3 s

Sound wave travelling a distance of

45 m

with the speed of

340 m / s

will take time,

t_{2}

t_{2} = \frac{h}{v}

\Rightarrow t_{2} = \frac{45}{340}

\Rightarrow t_{2} = 0.13 s

And hence, total time,

t = t_{1} + t_{2}

\Rightarrow t = 3 + 0.13

\Rightarrow t = 3.13 s

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