To determine the minimum distance required for hearing an echo, we need to understand the relationship between the speed of sound, the time it takes for the echo to be heard, and the distance the sound travels.
1. Speed of Sound: The speed of sound is provided as [tex]\(344 \, \text{m/s}\)[/tex].
2. Time for Echo: The echo is heard after a certain time. For this problem, it is stated to be [tex]\(0.1\)[/tex] seconds.
3. Distance Calculation:
- The sound travels to the obstacle and then reflects back, so the total distance the sound wave covers is twice the distance between the source and obstacle.
- We use the formula for distance: [tex]\( \text{distance} = \text{speed} \times \text{time} \)[/tex].
The total distance covered by the sound wave is:
[tex]\[
\text{total distance} = 344 \, \text{m/s} \times 0.1 \, \text{s} = 34.4 \, \text{meters}
\][/tex]
4. Minimum Distance to the Obstacle:
- Since the sound has to travel to the obstacle and back to the source, the minimum distance to the obstacle is half of the total distance calculated:
[tex]\[
\text{minimum distance} = \frac{34.4 \, \text{meters}}{2} = 17.2 \, \text{meters}
\][/tex]
Therefore, the minimum distance of the obstacle from the source of sound for hearing an echo is:
[tex]\[
\boxed{17.2 \, \text{m}}
\][/tex]
The correct option is (B) 17.2 m.
