Echo Distance Calculation

To hear an echo clearly, the reflected sound must reach the listener at least 0.1 seconds after the original sound. This time difference allows the human ear to distinguish the two sounds.

The sound travels to the reflecting surface and back to the listener. Therefore, the total distance covered by the sound is twice the distance to the surface.

Required Physics Concepts

• Speed of sound (\(v\)) is approximately \(340 \, \text{m/s}\).
• Minimum time (\(\Delta t\)) for sound perception is \(0.1 \, \text{s}\).
• Relationship: Distance = Speed × Time.

Calculation Steps

1. Determine the total distance the sound must travel. This is twice the distance (\(d\)) to the reflecting surface, so \(2d\).
2. Use the formula: \(2d = v \times \Delta t\).
3. Substitute the known values: \(2d \approx 340 \, \text{m/s} \times 0.1 \, \text{s}\).
4. Calculate the total distance: \(2d \approx 34 \, \text{m}\).
5. Calculate the distance to the reflecting surface: \(d = \frac{34 \, \text{m}}{2}\).
6. Result: \(d = 17 \, \text{m}\).

Therefore, the reflecting surface should be at least 17 m from the listener to hear the echo clearly.