What minimum distance is required between the source of sound and the reflecting surface to hear the echo? Give reason.

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Solution

We know that the speed of sound in air is nearly 330 m  $s^{- 1}$ . To hear an echo, the sound after reflection from a surface should reach at least 0.1 s after the original sound is heard. This is because the original sound persists in the human ear for about 0.1 s.

In 0.1 s, the sound will travel a distance = 330 m $s^{- 1}$ x 0.1 s = 33 m.

Since sound has to travel an equal distance in going up to the reflecting surface and in coming back from the reflecting surface, therefore it must travel nearly, $\frac{33}{2}$ = 16.5 m, either way.

Thus, to hear the echo clearly in air, the reflecting surface should be at a minimum distance of 16.5 m from the source of sound.

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