### Theory:

An echo is a sound that is reproduced due to the original sound being reflected off from various rigid surfaces such as walls, ceilings, mountain surfaces, and so on.
Shouting near a mountain

You can hear the same sound if you shout or clap near a mountain or a reflecting surface, such as a building. The sound you hear is known as an echo. It is because of sound reflection. In a small room, there is no possibility of echo. This situation does not mean that sound bounces around in a small space. This is due to the fact that smaller rooms do not meet the basic requirements for hearing an echo.

Conditions necessary for hearing the echo:
• Human ears have a $$0.1$$ $$-$$ $$second$$ persistence of hearing. This means that if the time interval between two sounds is at least $$0.1$$ $$s$$, you can hear both of them. As a result, the time gap between the original sound and the echo must be at least $$0.1$$ $$seconds$$.
• The above criterion can be met if the distance between the source of sound and the reflecting surface obeys the following equation:
$\begin{array}{l}\mathit{Velocity}=\frac{\mathit{Distance}\phantom{\rule{0.147em}{0ex}}\mathit{travelled}\phantom{\rule{0.147em}{0ex}}\mathit{by}\phantom{\rule{0.147em}{0ex}}\mathit{sound}}{\mathit{Time}\phantom{\rule{0.147em}{0ex}}\mathit{taken}}\\ v=\frac{2d}{t}\\ d=\frac{\mathit{vt}}{2}\end{array}$
since, $\begin{array}{l}t=0.1\phantom{\rule{0.147em}{0ex}}\mathit{second},\phantom{\rule{0.147em}{0ex}}\mathit{then}\\ d=\frac{v×0.1}{2}\\ d=\frac{v}{20}\end{array}$
As a result, the minimum distance required to hear an echo is $1/{20}^{\mathit{th}}$ part of the magnitude of sound velocity in air. If you consider the velocity of sound as $$344$$ $m/s$s, the minimum distance required to hear an echo is $$17.2$$ $$m$$.

Application of echoes:
• Some animals use sound signals to communicate and locate objects over long distances.
• Obstetric ultrasonography, which creates real-time visual images of the developing embryo or foetus in the mother's uterus, uses the echo principle. Because it does not use any harmful radiation, this is a safe testing tool.
• In any medium, echo is used to determine the velocity of sound waves.