Question

A man pronounces $a,b,c,d$ and $e$ and hears last four syllables as an echo. Taking velocity of sound as $340m{s}^{-1}$, the distance of reflecting surface, if it takes one-fifth of a second to pronounce or hear one syllable is

• A. $136m$
• B. $316m$
• C. $613m$
• D. $340m$

Answer 1

The correct option is A $136m$

Let the distance between the man and the reflecting surface be $x$ metres.

Thus the distance travelled by sound to reach back to the man $d=2x$

The man cannot hear the syllable $a$ as at the instant when echo of syllable $a$ is about to reach to the man, he pronounces $e$. Thus the time taken by man to pronounce all syllables is equal to the time taken by the sound to reach back to the man. i.e $t=4\times \frac{1}{5}=\frac{4}{5}sec$

Thus $d=vt$

$2x=340\times \frac{4}{5}⟹x=136m$