Question

What is the maximum persistence of hearing for human beings?
${\text{A}}{\text{.}}$ 1 s
${\text{B}}{\text{.}}$ $\dfrac{1}{5}$ s
${\text{C}}{\text{.}}$ $\dfrac{1}{{10}}$ s
${\text{D}}{\text{.}}$ $\dfrac{1}{2}$ s

Answer 1

Hint: Here, we will proceed by defining the term echo. Then, we will discuss when the echo produced by the source will be heard distinctly (i.e., minimum distance conditions required).

Complete Step-by-Step solution:
Sound waves can be mirrored as can all waves. Sound waves are suffering from the large obstacles to reflection. The sound that is called an echo is heard as a result of reflection of sound waves from a large obstacle. As the reflected sound gets merged with the original sound, echo is usually not heard. To hear an echo clearly (as a separate sound) must be satisfied with certain conditions.
For around 0.1 seconds the sense of every sound remains in our ear. That is known as hearing persistence. If the echo is heard during this time span it is difficult to differentiate the original sound and its echo.
So the most important condition for hearing an echo is that only after a lapse of at least 0.1 seconds after the original sound dies off, should the reflected sound reach the ear. As, the vacuum velocity of the sound is c = 340 m/s.
Since, Distance travelled = $Speed\times Time$
Distance travelled by sound = $\text{ Speed of light}\times \text{Time taken}$
Distance travelled by sound in 0.1 second = $340\times 0.1$ = 34 m
Within 0.1 second the distance traveled by sound will be equal to 34 m. The minimum distance between a sound source and the reflector is twice that. And if the barrier is at least 17 m away, the reflected sound or the echo can be heard clearly after 0.1 second.
Therefore, the maximum persistence of hearing for human beings is equal to 0.1 seconds or $\dfrac{1}{{10}}$ s.
Hence, option C is correct.

Note- Hearing is the process through which the ear transforms the external environment's sound vibrations into nerve impulses that are transmitted to the brain where they are interpreted as sounds. Sounds are produced when objects that vibrate, such as a guitar's plucked string, produce pressure pulses from vibrating air molecules, better known as sound waves.