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When do we hear an echo?

The echo depends on the temperature of the surroundings and the distance between you and the point of reflection. Assume that the temperature of the surroundings is approximately 𝟐𝟐^∘𝑪. At this temperature, the distance between you and the wall has to be at least 17.2 m for you to hear an echo. Only if it is equal to or greater than 17.2 m, you may hear an echo.

Minimum distance required to hear an Echo

We can even verify the above-mentioned condition mathematically.

Let’s consider that the sound wave is incident perpendicular to the surface rather than at an

angle. This is just to simplify things.

One important point to note is that the sound that we hear persists in our minds for 0.1 seconds. It means the sensation of any sound that we hear lasts in our mind only for 0.1

seconds.

This means that we hear an echo because the reflected sound arrived at our ear after a time greater than 0.1 second.

When you clap once, you hear the sound. To hear the repetition of this sound, the time interval between the original sound and the reflected sound must be at least 0.1 seconds.

Now we need to find out why the distance between you and the obstacle should be at least

17.2 m for you to hear an echo. So what we will do is calculate this distance using our speed- distance-time formula.

Let this distance be ‘d’ m.

Minimum distance calculation to hear an Echo

We know that the speed of sound, ‘v’, in air at 𝟐𝟐^∘𝑪 is around 344 m/s. Speed (v) = 344m/s

And the time, ‘t’, for a wave to travel towards the wall and back is either greater than or equal

to 0.1 seconds. Time lapse(𝒕) ≥ 𝟎. 𝟏𝒔

In this time, the wave is covering twice the distance as it travels to this point and comes back. That is, in 0.1 seconds the sound wave is covering a distance of ‘2d’ m.

𝟐𝒅 = 𝒗 × 𝒕

We know that ‘t’ is greater than or equal to 0.1 seconds. And ‘v’ is constant. Thus, the above

equation can also be written as

𝟐𝒅 ≥ 𝟑𝟒𝟒𝒎/𝒔 × 𝟎. 𝟏𝒔

On dividing both the sides by two we get ‘d’ as greater than or equal to 17.2 m.

𝒅 ≥ 𝟏𝟕. 𝟐𝒎

Hence we say that the distance between you and the wall should be at least 17.2 meters at a temperature of 𝟐𝟐^∘𝑪 for you to hear an echo.

We know that the speed of the sound increases on increasing the temperature. Thus, on increasing the temperature the speed of sound will increase and thereby increasing the distance required to hear an echo.