the minimum distance between the reflecting surface and source for listening the eco of sound is ( take speed of sound 340` m/s`)

Options

A. 34 m
B. 8.5 m
C. 17 m
D. 28 m

Answer

To find the minimum distance between the reflecting surface and the source for listening to the echo of sound, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Problem**: We need to determine the minimum distance between a sound source and a reflecting surface (like a wall) so that the echo can be heard clearly. The speed of sound is given as 340 m/s.

2. **Use the Time of Persistence of Hearing**: The human ear can perceive an echo if the time taken for the sound to travel to the reflecting surface and back is at least 0.1 seconds.

3. **Calculate the Total Distance**: The total distance traveled by the sound (to the reflecting surface and back) can be expressed as:
\[ \text{Total Distance} = 2d \]
where \( d \) is the distance from the source to the reflecting surface.

4. **Relate Distance, Speed, and Time**: The relationship between distance, speed, and time is given by:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
Therefore, we can write:
\[ 2d = V \times t \]
where \( V = 340 \, \text{m/s} \) and \( t = 0.1 \, \text{s} \).

5. **Substitute Values**: Substitute the values into the equation:
\[ 2d = 340 \, \text{m/s} \times 0.1 \, \text{s} \]

6. **Calculate the Total Distance**:
\[ 2d = 34 \, \text{m} \]

7. **Solve for \( d \)**: To find the minimum distance \( d \):
\[ d = \frac{34 \, \text{m}}{2} = 17 \, \text{m} \]

### Final Answer:
The minimum distance between the reflecting surface and the source for listening to the echo of sound is **17 meters**.

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