Question

A man stands in a narrow, steep-sided valley. When he shouts he hears two echoes, one after $l$ s and other after $2s$. If the velocity of sound in air is $330m/s$, 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
$2s_1=v{t}_1$ and $2s_2=v{t}_2$
$\Rightarrow 2(s_1+s_2)=v(t_1+t_2)$
$\Rightarrow s_1+s_2=\frac{v(t_1+t_2)}{2}$
$\therefore d=s_1+s_2$
$=\frac{330\times (1+2)}{2}$
$\Rightarrow d=\frac{330\times 3}{2}=495m$