Question

A boy is standing in the middle of a big square field . There is a tall building on one side of the field . He explodes a cracker and hears its 0.45 seconds later . What is the size of the square field

Answer 1

$A=23823.9225\ m^2$ is the area of the field.

Explanation:

Given that a boy is in the center of a square field.

Time lag between the explosion of cracker and the echo being heard, $\Delta t=0.45\ s$

We have the speed of sound in the air, $v=343\ m.s^{-1}$

Now the distance of the covered by the reflected sound wave during this period:

$d=v.\Delta t$

$d=343\times 0.45$

$d=154.35\ m$

The actual distance of the sound source will be half of this distance because the sound has to travel to-and-fro form the source.

$s=\frac{d}{2}$

$s=\frac{154.35}{2}$

$s=77.175\ m$

The double of this distance will be the length of a side of the square(because the sound source is at the center of this field):

$l=2s$

$l=154.35\ m$

Therefore, area of the square field,

$A=l\times l$

$A=154.35^2$

$A=23823.9225\ m^2$

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TOPIC: echo of sound

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