To hear an echo, the minimum distance between the source of sound and the reflecting surface should be at least 17 meters. This is because the sound wave must travel to the reflecting surface and back to the listener.
Here’s the reasoning:
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Speed of Sound: The speed of sound in air is approximately 343 meters per second (at room temperature).
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Time Delay for Echo: For a distinct echo to be heard, there should be a minimum time interval between the original sound and the reflection. This time interval is typically considered to be at least 0.1 seconds.
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Calculating Distance:
- During this time (0.1 seconds), the sound travels to the reflecting surface and back. Therefore, the total distance traveled by the sound wave is the distance to the reflecting surface multiplied by two (to account for the journey to the surface and back).
- Using the speed of sound, the distance can be calculated as: \[ \text{Distance} = \text{Speed} \times \text{Time} \] \[ \text{Total Distance} = 343 , \text{m/s} \times 0.1 , \text{s} = 34.3 , \text{meters} \] Since this is for the round trip, the one-way distance to the reflecting surface should be half of this: \[ \text{One-way Distance} = \frac{34.3}{2} = 17.15 , \text{meters} \]
Therefore, the minimum distance between the source of sound and the reflecting surface to hear a clear echo should be at least 17 meters.