Question

A girl is sitting in the middle of a park of dimension $12m\times 12m$. On the left side of it, there is a building adjoining the park and on the right side of the park, there is a road adjoining the park. A sound is produced on the road by a cracker. Is it possible for the girl to hear the echo of this sound? Explain your answer.

Answer 1

Step 1: Given data

The minimum time for which an echo should travel to be heard by the listener is $0.1s$.

Speed of sound in the air is $344m{s}^{-1}$

The diagrammatic representation of the given data is:

Step 2: Calculate the minimum distance that must be travelled by an echo

As we know, $Dis\tan ce=speed\times time$

The minimum distance that needs to be travelled by the sound to be heard as an echo is $344\times 0.1=34.4m$

Step 3: Calculate the actual distance travelled by the sound of the crack in the road

Here, the sound first travels from road to building, then gets reflected by the building and then it will be listened to by the girl as an echo.

So, the actual distance travelled by the sound is $12+6=18m$.

As the actual distance travelled is less than the required distance i.e., $18<34.4$, the echo of the sound of the crack in the road will not be heard by the girl.

Hence, the girl cannot hear the echo of the sound of the crack in the road for the given case.