Question

A man is standing at a distance of 48 m away from a wall. He fires a gun and hears
a distinct echo. Every time he fires the gun, he takes a step forward and repeats
the same. What is the maximum displacement of he man from his initial position
towards the wall for which he gets a distinct echo? [ Speed of Sound in air is
320 m/s ]

Answer 1

Answer:

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Explanation:

Like all waves, sound waves can be reflected. Sound waves suffer reflection from the large obstacles. As a result of reflection of sound wave from a large obstacle, the sound is heard which is named as an echo. Ordinarily echo is not heard as the reflected sound gets merged with the original sound. Certain conditions have to be satisfied to hear an echo distinctly (as a separate sound).

The sensation of any sound persists in our ear for about 0.1 seconds. This is known as the persistence of hearing. If the echo is heard within this time interval, the original sound and its echo cannot be distinguished. So the most important condition for hearing an echo is that the reflected sound should reach the ear only after a lapse of at least 0.1 second after the original sound dies off.

As the speed of sound is 320 m/s and the distance traveled by sound is 48 m. This is twice the minimum distance between a source of sound and the reflector. So, if the obstacle is at a distance of 17 m at least, the reflected sound or the echo is heard after 0.1 second, distinctly.

As the speed of sound is 320 m/s and the distance traveled by sound is 48 m are given in the question, the time taken is calculated from the formula,

Timetaken=

velocityofsound

Distancetraveled

.

The total distance traveled by the sound is given as 2×48 m as it is reflected sound.

The time taken for the echo to be heard is =

320m/s

2×48m

= 0.3 s.