Question

A man stands in a narrow, steep-sided valley. When he shouts he hears two echoes, one after 1 sand other after 2s. If the velocity of sound in air is 330 m/s, the width of the valley is

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

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 $2s_2=v{t}_2$ $\Rightarrow$ $2(s_1+s_2)=v(t_1+t_2)$ $\Rightarrow$ $s_1+s_2=\frac{v(t_1+t_2)}{2}$ $\therefore$ $d=s_1+s_2=\frac{330\times (1+2)}{2}$ $\Rightarrow$ $d=\frac{330\times 3}{2}=495m$