Minimum Distance to Hear an Echo

In this post, we will calculate the minimum distance required to hear an echo. But before that, we will briefly find out the concepts of echo.

Minimum Distance to Hear an Echo – calculation

Echo – What is an echo?

The repetition of sound caused by the reflection of sound waves is referred to as an echo. When a person shouts in a spacious empty hall, we first hear his original sound. After a little while, we hear the reflected sound of the shout. This ‘reflected sound’ is an ‘echo’.

So, when we hear an echo, we are actually hearing a reflected sound, a short while after the original sound. Thus, an echo is simply a reflected sound. An echo is heard when sound is reflected from a hard surface such as a tall brick wall or a cliff. A soft surface tends to absorb sound, so there is no echo.

Calculating the Minimum Distance to Hear an Echo

Scientists have estimated that if two sounds reach our ears within an interval of 1/10th of a second, then we cannot hear them as separate sounds, as they appear to be just one sound.
The human ear can hear two sounds separately only if there is a time interval (or time gap) of 1/10th of a second (or more) between the two sounds.

This means that we can hear the original sound and the reflected sound (echo) separately only if there is a time interval (or time gap) of at least 1/10th of a second (or 0.1 seconds) between them.

Now, knowing the minimum time interval required for an echo to be heard and the speed of sound in air, we can calculate the minimum distance from a sound-reflecting surface (like a wall, etc.) which is necessary to hear an echo.

These calculations are given below :

Speed = Distance traveled/Time taken ……………………………… [1]
=> Distance traveled = speed x Time taken ……………………………[2]

Here, Speed of sound = 344 m/s (at 20°C)
Distance traveled = d (We will calculate now)
And, Time duration = 1/10 s = 0.1 s

Now, putting these values in equation [2] above, we get :
Distance traveled = speed x Time taken
=>d = 344 x [1/10] m = 34.4 m

Thus, the distance traveled by sound in 1/10th of a second is 34.4 meters.

But this distance is traveled by sound going from us (the source of sound) to the sound-reflecting surface (like a wall) and then coming back to us (the source and also the listener).

So, our distance from the sound-reflecting surface (like a wall, etc.) to hear an echo should be half of 34.4 meters which is 34.4/2 =17.2 meters.

Conclusion:

From this, we can conclude that the minimum distance from a sound-reflecting surface (wall, etc.) to hear an echo is 17.2 meters (at 20°C). This means that in order to hear an echo of our shout, we should be at least 17.2 meters away from a sound-reflecting surface like a wall.