Question

A man standing 48m away from a wall fires a gun. Calculate the time after which an echo is heard. (The speed of sound in air is $320m{s^{ - 1}}$).
(A) $0.38$
(B) $0.30$
(C) $0.50$
(D) $0.60$

Answer 1

Hint: Echo is repetition or imitation of sound when sound waves hit a hard surface they right reflect, making the sound bounce and repeat.
When we walk in hospitals or school corridors we hear footsteps of our own.That the sound which we are able to hear is called echo.

Complete step by step answer:
Like all waves, sound waves can be reflected sound waves suffer reflection of sound waves from a large obstacle, the sounds heard which is called echo. Ordinary echo is not heard if the reflected wave gets merged with the original sound containing condition and has to be satisfied to hear on echo as a separate sound.
The separation of any sound persists in our echo for about $0.1$seconds. This is proven as persistence of hearing. If the echo is heard within this time, the original sound and its echo cannot be distinguished. So the most important condition of hearing on echo is that the reflected sound would reach ears only after a lapse of at least $320m/s$ and distance travelled by wave is $48m.$ This is twice the minimum distance between a sound of wave and the distance of $17m$ at least, the reflected sound or echo is heard after $0.1$ sound,
As speed of wave is $320m/s$ and travelled a distance of $48m,$the time taken is calculated by
Time taken $ = \dfrac{{Dis\tan ce\,traveled}}{{velocity\,of\,wave}}$
The total distance travelled by sound is given as $2 \times 48m$ as it is reflected wave time taken by echo is $ = \dfrac{{2 \times 48}}{{320}} = 0.3$ seconds.
Hence, the answer is $0.3$ seconds.

So, the correct answer is “Option B”.

Note:
We may not hear any echo if the time taken by other or repeating sound waves is not $0.1$ seconds after the original sound so we need a repeating sound to be at a time lapse of $0.1$ seconds from the original sound.
The most important condition of hearing on echo is that the reflected sound would reach ears only after a lapse of at least.