Question

A man stands in a narrow, steep-sided valley. When he shouts he hears two echoes, one after l s and other after 2 s. If the velocity of sound in air is 330 m/s, the width of the valley is

• A. 330 m
• B. 495 m
• C. 660 m
• D. 990 m

Answer 1

The Correct Option is B

Let $s_1$ and $s_2$ be the distances of man from either side of valley,
then

$\hspace35mm 2s_1 =vt_1$ and $2s_2 = vt_2$
$\Rightarrow \hspace15mm 2(s_1 + s_2)=v(t_1 + t_2)$
$\Rightarrow \hspace20mm s_1 + s_2= \frac{v(t_1 + t_2)}{2}$
$\therefore \hspace25mm d = s_1 + s_2 $
$ \hspace32mm = \frac{330 \times (1+2)}{2}$
$\Rightarrow \hspace25mm d = \frac{330 \times 3}{2} = 495\, m$