Question

The speed of sound in air is 330 m/s and the human brain can only distinguish sounds 0.1 s apart. A person is standing beside a source of the sound. What should be the minimum distance between the source and the reflecting surface for the echo to be heard by him?

• A. 33 m
• B. 16.5m
• C. 34m
• D. 15m

Answer 1

The correct option is B

16.5m

We know the sensation of sound persists in our brain for 0.1 s. So to hear an echo, the time interval between the original sound and reflected one must be at least 0.1 s.

The person is standing beside the source of the sound.

Speed of sound (Given) = 330 m $s^{-1}$

Let $d$ be the distance between the source and the reflecting surface.

So, total distance travelled by the reflected sound wave = $2d$

$2d=vt$

$v$ velocity of sound. $t$ time by the reflected wave to cover distance $2d$.

The distance between the source and the object is minimum if the total time taken is 0.1 s.

The minimum distance $d_m$ is given by

$2d_m=330\times 0.1$

$d_m=16.5m$