Question

State whether the given statement is True or False:
A girl is sitting in the middle of a park of dimension 12 m x 12 m. 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. The girl will be able to hear the echo of this sound.
A. True
B. False

Answer 1

Echo is defined as the reflection of the sound wave that the listener perceives clearly, after the sound waves bounces off a hard surface. Whenever the sound waves are produced, they do reflect across objects around us and our ears do receive the sound. But our human ear cannot perceive the reflection of the sound and hence, does not classify as echo.

Complete step-by-step answer:
Our ears can perceive the echo sound if it is reflecting back with a difference of 0.1 second. We know that the speed of sound in air is $340m{s^{ - 1}}$. So, the minimum distance that the sound has to travel in order to hear the echo,
$D = s \times t \\\ D = 340 \times 0.1 \\\ D = 34m \\\$
This distance includes the to and fro movement of the sound waves in the echo.
Thus, the minimum distance that the obstacle has to be present to hear an echo,
$d = \dfrac{D}{2} \\\ d = \dfrac{{34}}{2} \\\ d = 17m \\\$
In this problem, the girl is sitting in the middle of the park and the cracker sound is produced in the road on the left side.

From the diagram, it is clear that the sound has to travel a total of $6 + 6 = 12m$ from the girl to the cracker and back.
However, this is less than the minimum distance requirement for echo, which is $17m$.
Therefore, there will be no echo.

Hence, the correct option is Option 2 – FALSE.

Note: Sometimes, you might get a similar problem with the park dimensions 15x15 m and the girl is sitting on the one edge of the park instead of the park. In such a case, you should not be misled by the given value of 15 m because it is only one-way distance. Since, it takes 30m for the to and fro motion of sound waves after the reflection, there is a definitive echo in that case.