Question

To hear a distinct echo, the minimum distance of reflecting surface should be:
A. 7m
B. 17m
C. 27m
D. 10m

Answer 1

Hint: The phenomena of hearing a sound twice, when it is reflected back from a distance obstacle is called echo. Humans need at least $0.1\sec $ to distinctly hear a sound, with the speed of sound and the distance formula, this question can be answered.

Complete step-by-step answer:
The phenomena of hearing a sound twice, when it is reflected back from a distance obstacle is called echo. If you go to a hill station, and shout in front of a mountain, then a few seconds back you will hear your own voice. This is because of echo. This is a very common simple yet mesmerizing phenomena. But wait, if that is true why don't we hear echo all the time when we speak? The reason is that a human ear can distinguish sounds which are at least $0.1\sec $ apart. So, if the same sound enters our ear our brain can't distinguish them. That is technically we hear echo all the time but can't perceive it. So, in order to hear echo, the sound must return after 0.1 sec.
Simple, speed distance formula can be applied here.
That is
$\text{distance}=\text{speed}\times \text{time}$
Where, we take the speed of sound in air to be $344m{{s}^{-1}}$,
Therefore, the distance it is supposed to travel is:
$\begin{align}
  & \text{distance}=\text{speed}\times \text{time} \\
 & \text{distance}=344\times 0.1=34.4m \\
\end{align}$
Since, the sound travels forwards and backwards, the distance of the wall from the person is half the distance the sound travels.
Therefore, the wall must at least be at $\dfrac{34.4}{2}=17.2$ m from the person in order to hear an echo.
Note: As you know sound is a mechanical-longitudinal wave, and in air it travels at the speed of $344m{{s}^{-1}}$. The speed of sound is different in different mediums like water or any other gas, in such situations, the answer will be different depending on the density of medium, like in water sound travels faster and hence the distance should be greater than what we got.