A girl is sitting in the middle of a park of dimension 12 m × 12 m. On the left side of it there is a building adjoining the park and on 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.

Question

A girl is sitting in the middle of a park of dimension 12 m × 12 m. On the left side of it there is a building adjoining the park and on 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.

Philoid · Accepted Answer

To hear a distinct echo the time interval between the original sound and the reflected one must be at least 0.1 s.

If we take the speed of sound to be 344 m/s at a given temperature, say at 2^o C in air, the sound must go to the obstacle and reach back the ear of the listener on reflection after 0.1 s. Hence, the total distance covered by the sound from the point of generation to the reflecting surface and back should be at least (344m/s) * 0.1s = 34.4 m.

Thus, for hearing distinct echoes, the minimum distance of the obstacle from the source of sound must be half of this distance, that is, 17.2 m.

But in this case, the distance traveled by the sound reflected from the building and then reaching to the girl will be (6 + 6) = 12 m. That is, the minimum distance of the obstacle from the source of sound is 6 m, which is much smaller than the required distance (17.2 m). Therefore, no echo can be heard.