Question

How far away is the cliff from the child, if a child hears an echo from a cliff 6 seconds after the sound produced by a powerful horn? The velocity sound in air at $22{\text{ }}^\circ C$ is $344$ m/s.

Answer 1

Echo is a sound reflection that comes at the listener with a delay after the direct sound in audio signal processing and acoustics. The delay is related to the distance between the source and the listener of the reflecting surface. The echo generated by the bottom of a well, a building, or the walls of an enclosed room and an empty room are all good examples. A genuine echo is a single sound source reflection.
${\text{velocity = }}\dfrac{{{\text{to and fro distance}}}}{{{\text{time}}}}$ .

Complete answer:
Walls and other hard surfaces, such as mountains and privacy fences, reflect acoustic waves. A discontinuity in the propagation medium might be the cause of reflection. When the reflection returns with enough magnitude and latency to be heard clearly, this can be heard. The echo is described as a reverberation when sound, or the echo itself, is reflected many times from multiple surfaces. If the delay is shorter than a tenth of a second, the human ear cannot discriminate between echo and the original direct sound. At a temperature of $25{\text{ }}^\circ C$ , the sound velocity in dry air is roughly 343 m/s.
As a result, for a person standing at the source to hear an echo, the reflecting item must be more than 17.2 metres away. The reflecting object is 343 metres distant when a sound creates an echo in two seconds. The most typical natural environments for hearing echoes are canyon walls or rock cliffs facing water. The sound pressure level (SPL) of an echo is usually measured in decibels (dB) in comparison to the directly transmitted wave. Echoes can be beneficial (as in sonar) or harmful (as in telephone systems).
Let d m be the distance between the cliff and the child. The entire distance travelled by the sound is then equal to 2d, and the total time consumed is equal to 6 s.
${\text{velocity = }}\dfrac{{{\text{to and fro distance}}}}{{{\text{time}}}}$
Then, ${\text{sound velocity = }}\dfrac{{{\text{2d}}}}{{{\text{6s}}}}{\text{ = }}\dfrac{{\text{d}}}{{{\text{3s}}}}$
$344{\text{ }}m{s^{ - 1}}{\text{ }} = {\text{ }}\dfrac{d}{3}$
$d = 344 \times 3 = 1032m$
Hence the distance is 1032 m.

Note:
Note that in echo the distance is simply not d, but referred to as 2d. The term echo comes from a Greek word that means "to echo." Echo is a mountain nymph whose power to speak was cursed, leaving her only able to repeat the last words uttered to her in a Greek folk tale. Cetaceans (dolphins and whales) and bats, for example, employ echo for location sensing and navigation.