The minimum distance to hear echo (speed of sound in air is `340 m//s`)

Options

A. `15 m`
B. `16 m`
C. `17 m`
D. `18 m`

Explanation

To find the minimum distance required to hear an echo, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Echo**: An echo is heard when sound waves reflect off a surface and return to the listener. For an echo to be heard, the sound must travel to the obstacle and back.

2. **Distance Calculation**: If the distance to the obstacle is \(d\), then the total distance traveled by the sound is \(2d\) (to the obstacle and back).

3. **Speed of Sound**: The speed of sound in air is given as \(v = 340 \, \text{m/s}\).

4. **Time for Echo**: For a person to hear the echo, the time taken for the sound to travel to the obstacle and back must be at least 0.1 seconds (or 1/10 of a second).

5. **Using the Formula**: The relationship between distance, speed, and time is given by the formula:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
Therefore, for the echo:
\[ 2d = v \times t \]
where \(t\) is the time taken for the echo to return.

6. **Setting Time**: We set \(t = 0.1 \, \text{s}\) (the minimum time to hear the echo):
\[ 2d = v \times 0.1 \]

7. **Substituting Values**: Now substituting \(v = 340 \, \text{m/s}\):
\[ 2d = 340 \times 0.1 \]
\[ 2d = 34 \, \text{m} \]

8. **Solving for \(d\)**: Now, divide both sides by 2 to find \(d\):
\[ d = \frac{34}{2} = 17 \, \text{m} \]

### Final Answer:
The minimum distance to hear an echo is **17 meters**.