A man standing 25 m away from a wall produces a sound and receives the reflected sound. (a) Calculate the time after which he receives the reflected sound if the speed of sound in air is 350 ms^-1. (b) Will the man be able to hear a distinct echo? Explain the answer.

(a) As we know,

$\text {Speed of sound (V)} = \dfrac{\text{Total distance travelled (2d)}}{\text {time interval (t)}} \\[0.5em]$

Total distance travelled by the sound in going and then coming back = 2d

Given,

d = 25 m

V = 350 ms^-1

Substituting the values in the formula above, we get,

$350 = \dfrac{2 \times 25}{t} \\[0.5em] \Rightarrow t = \dfrac{50}{350} \\[0.5em] \Rightarrow t = \dfrac{1}{7} \\[0.5em] \Rightarrow t = 0.143 s \\[0.5em]$

Hence, the time after which he receives the reflected sound = 0.143 seconds

(b) Yes, the man will be able to hear a distinct echo.
As an important condition for hearing an echo is that the reflected sound should reach the ear only after a lapse of at least 0.1 s because original sound persists only for 0.1 s. Hence, a distinct echo is heard because the man receives the reflected sound after 0.143 seconds.