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

Answer: (B)

Let $s_1$ and $s_2$ be the distances of man from either side of valley, then
$ 2s_1 =vt_1$ and $2s_2 = vt_2$
$\Rightarrow 2(s_1 + s_2)=v(t_1 + t_2)$
$\Rightarrow s_1 + s_2= \frac{v(t_1 + t_2)}{2}$
$\therefore d = s_1 + s_2 $
$= \frac{330 \times (1+2)}{2}$
$\Rightarrow d = \frac{330 \times 3}{2} = 495\, m$