An echo will be heard if the minimum distance between the source of sound and the obstacle is

Options

A. 1 m
B. 10 m
C. 15 m
D. 17 m

Answer

To find the minimum distance between the source of sound and the obstacle for an echo to be heard, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Concept of Echo**:
- An echo is heard when the sound waves reflect off an obstacle and return to the listener. For a person to hear the echo, the reflected sound must reach them after a certain time.

2. **Persistence of Hearing**:
- The human ear can perceive an echo if the time interval between the original sound and the reflected sound is at least 0.1 seconds. This is known as the persistence of hearing.

3. **Distance Calculation**:
- Let \( d \) be the distance from the source of sound to the obstacle. The sound travels to the obstacle and back, so the total distance traveled by the sound is \( 2d \).

4. **Using the Speed of Sound**:
- The speed of sound in air is approximately 340 meters per second (m/s).

5. **Setting Up the Equation**:
- The time taken for the sound to travel to the obstacle and back can be expressed as:
\[ \text{Time} = \frac{\text{Total Distance}}{\text{Speed}} = \frac{2d}{340} \]
- For the echo to be heard, this time must be at least 0.1 seconds:
\[ \frac{2d}{340} \geq 0.1 \]

6. **Solving for \( d \)**:
- Rearranging the equation gives:
\[ 2d \geq 0.1 \times 340 \]
- Calculating the right side:
\[ 0.1 \times 340 = 34 \]
- Therefore:
\[ 2d \geq 34 \]
- Dividing both sides by 2:
\[ d \geq \frac{34}{2} = 17 \text{ meters} \]

7. **Conclusion**:
- The minimum distance between the source of sound and the obstacle for an echo to be heard is **17 meters**.